Let S be the subspace of R3 given by S = Span *** ((:)) 2 Find a basis for S.
Answers
A basis for S is {a, b} = {(1, 2, 0), (-1, 1, 2)}.
In the given question, S is the subspace of R3 given by S = Span{a, b}, where a = (1, 2, 0) and b = (-1, 1, 2). We need to find a basis for S.A basis for S can be defined as the minimum set of vectors that span S.
Therefore, to find a basis for S, we need to check whether {a, b} is a linearly independent set or not.
Linearly independent set: A set of vectors {v1, v2, ..., vn} is linearly independent if the only solution to the equation a1v1 + a2v2 + ... + anvn = 0 is a1 = a2 = ... = an = 0.
If there are other non-zero solutions, then the set of vectors is linearly dependent. This means that at least one vector in the set can be represented as a linear combination of the others.In the given problem, we will solve the equation a1a + a2b = 0, where a1 and a2 are scalars.If we take a1 = 1 and a2 = -1, then a1a + a2b = (1)(1, 2, 0) + (-1)(-1, 1, 2) = (2, 1, -2).
Since (2, 1, -2) is not equal to the zero vector, this implies that {a, b} is a linearly independent set. Hence, {a, b} is a basis for S.Therefore, a basis for S is {a, b} = {(1, 2, 0), (-1, 1, 2)}.
Hence, the solution is as follows:A basis for S is {a, b} = {(1, 2, 0), (-1, 1, 2)}.The above explanation can be formulated into a 150 words answer as follows:A basis for a subspace S of R3 can be found using the minimum set of vectors that spans the subspace S. In this problem, a subspace S of R3 is given by S = Span{a, b}, where a = (1, 2, 0) and b = (-1, 1, 2). We are required to find a basis for S.
To check whether {a, b} is a linearly independent set or not, we will solve the equation a1a + a2b = 0, where a1 and a2 are scalars.
On solving this equation, we get a1 = 1, a2 = -1, and (2, 1, -2) is not equal to the zero vector, which implies that {a, b} is a linearly independent set.
Therefore, {a, b} is a basis for S. Hence, a basis for S is {a, b} = {(1, 2, 0), (-1, 1, 2)}.
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Related Questions
What begins with T, ends with T, and has T in it?
Answers
Answer: A teapot.
Step-by-step explanation:
A school is ordering chairs for the teacher's lounge and some of the classrooms. Each classroom needs 17 chairs, while the teacher's lounge needs 16.
Let n represent the number of classrooms included in the order and c represent the total number of chairs. Complete the table using the relationship between n and c.
Answers
5515828288777776677
12
4. Consider 348 in decimal system. Convert the number directly from the decimal system to each of the following number systems. a) Binary System b) Octal System c) Hexadecimal System 151
Answers
a) The decimal number 348 is equivalent to 101011100 in the binary system.
b) The decimal number 348 is equivalent to 534 in the octal system.
c) The decimal number 348 is equivalent to 15C in the hexadecimal system.
a) To convert decimal to binary, we repeatedly divide the decimal number by 2 and note down the remainder. The binary equivalent is obtained by arranging the remainders in reverse order. In this case, dividing 348 by 2 gives a remainder of 0. Dividing the quotient (174) by 2 gives a remainder of 0 again. Continuing this process, we get the binary equivalent as 101011100.
b) To convert decimal to octal, we repeatedly divide the decimal number by 8 and note down the remainder. The octal equivalent is obtained by arranging the remainders in reverse order. In this case, dividing 348 by 8 gives a quotient of 43 and a remainder of 4. Dividing the quotient (43) by 8 gives a quotient of 5 and a remainder of 3. Finally, dividing 5 by 8 gives a quotient of 0 and a remainder of 5. The octal equivalent is 534.
c) To convert decimal to hexadecimal, we repeatedly divide the decimal number by 16 and note down the remainder. The hexadecimal equivalent is obtained by replacing remainders greater than 9 with the corresponding letters A to F. In this case, dividing 348 by 16 gives a quotient of 21 and a remainder of 12, which is represented as C. Dividing the quotient (21) by 16 gives a quotient of 1 and a remainder of 5. Finally, dividing 1 by 16 gives a quotient of 0 and a remainder of 1. The hexadecimal equivalent is 15C.
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you and 2 decide to each order a pizza for lunch would you rather
Answers
Answer:
My answer to the question is option B
Answer:
hmmmm Option A for me
Step-by-step explanation:
Rewrite 7 and 1/8 as an improper fraction.
Answers
Answer:
57/8
Step-by-step explanation:
PLEASE HELP I"LL GIVE BRAINLEST
Carl solves 12 multiplication problems for every 4 addition problems. If he solves 23 addition problems, how many multiplication problems does he solve?
46 multiplication problems
92 multiplication problems
69 multiplication problems
54 multiplication problems
Answers
Answer:
92 4× 23
Step-by-step explanation:
sorry if im incorrect
Answer:
Carl solves 69 multuplication problems
whats the scientific notation for 234,000,000
Answers
Answer:
scientific notation
= 2.34e8
scientific e notation
= 234 × 106
engineering notation
million; prefix mega- (M)
= 2.34 × 108
standard form
8
Order of Magnitude
for scientific and standard forms
= 234000000
(real number)
= two hundred thirty-four million
word form
Step-by-step explanation:
What’s the product of 728x32
Answers
Answer:
23296
Step-by-step explanation:
You will know this if you use box method or using standard form its pretty much simple multiplication
In Khan academy int he 8th grade section "Geometric transformation" in the section "Properties & definitions of transformations" how are you supposed to do this?
Answers
Answer:
First listen to the video on your left of the screen, and then on the right of your screen, you'll see tests. You click on the button below on the test that says practice and if you 3 out of 4 correct, you can do the other videos and tests.
Step-by-step explanation:
a set of data is normally distributed with a mean equal to 10 and a standard deviation equal to 3. calculate the z score for each of the following raw scores
Answers
The z-score is a standardized score that tells us how many standard deviations a data point is away from the mean. It is calculated as:
z = (x - mu) / sigma
where x is the raw score, mu is the mean, and sigma is the standard deviation.
For a normally distributed set of data with a mean of 10 and a standard deviation of 3, the z-score for each of the following raw scores would be:
x = 7
z = (7 - 10) / 3 = -1
The z-score for a raw score of 7 is -1.
x = 12
z = (12 - 10) / 3 = 0.67
The z-score for a raw score of 12 is 0.67.
x = 16
z = (16 - 10) / 3 = 2
The z-score for a raw score of 16 is 2.
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The cross partials of the function
z=f(x,y)=(x×y)2-ln(x×y)
are
fyx=
2xy-1/x2
fxy
≡-4xy
fyx≡0
fxy≡4xy
fxy=2xy-1/y2
Answers
Given function is
z=f(x,y)=(xy)²-ln(xy)
To find: fxy and fyx We have the function
z=f(x,y)=(xy)²-ln(xy)
Differentiate the function partially w.r.t x keeping y constant
f(x,y)=(xy)²-ln(xy)
Differentiating partially w.r.t x keeping y constant gives:
∂f/∂x = 2xy - (1/x)
equation (1)Differentiate the function partially w.r.t y keeping x constant
f(x,y)=(xy)²-ln(xy)
Differentiating partially w.r.t y keeping x constant gives:
∂f/∂y = 2yx - (1/y) equation
(2)Hence, the values of fxy and fyx are given by
fxy ≡ ∂²f/∂y∂x = ∂/∂y(2xy - (1/x)) = 2xfyx
∂²f/∂x∂y = ∂/∂x(2yx - (1/y)) = 2y
Therefore,
fxy = 2x
and f
yx = 2y
Thus, the correct options are:fxy ≡ 2xy-1/y2fyx ≡ 2xy-1/x2
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simplify the expression using the order of operations 4+(5-11) over 2^4 minus 14
You must show all your work.
Answers
Answer:
-1
Step-by-step explanation:
BEDMAS
\(\frac{4+(5-11)}{2^{4}-14 }\\\frac{4+(-6)}{16-14 }\\\frac{-2}{2}\\-1\)
Hope that helps
Suppose that the daily log return of a security follows the model rt = 0.02 +0.5rt-2 + et where {e} is a Gaussian white noise series with mean zero and variance0.02. What are the mean and variance of the return series rt? Compute the lag-1 and lag-2 autocorrelations of rt. Assume that r100 = -0.01, and r99 = 0.02. Compute the 1- and 2-step-ahead forecasts of the return series at the forecast origin t = 100. What are the associated standard deviation of the forecast errors?
Answers
Mean of rt = 0.02,
Variance of rt = 0.02,
Lag-1 Autocorrelation (ρ1) = -0.01,
Lag-2 Autocorrelation (ρ2) = Unknown,
1-step ahead forecast = -0.005,
2-step ahead forecast = 0.02,
The standard deviation of forecast errors = √0.02.
We have,
To find the mean and variance of the return series, we can substitute the given model into the equation and calculate:
Mean of rt:
E(rt) = E(0.02 + 0.5rt-2 + et)
= 0.02 + 0.5E(rt-2) + E(et)
= 0.02 + 0.5 * 0 + 0
= 0.02
The variance of rt:
Var(rt) = Var(0.02 + 0.5rt-2 + et)
= Var(et) (since the term 0.5rt-2 does not contribute to the variance)
= 0.02
The mean of the return series rt is 0.02, and the variance is 0.02.
To compute the lag-1 and lag-2 autocorrelations of rt, we need to determine the correlation between rt and rt-1, and between rt and rt-2:
Lag-1 Autocorrelation:
ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))
Lag-2 Autocorrelation:
ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))
Since we are given r100 = -0.01 and r99 = 0.02, we can substitute these values into the equations:
Lag-1 Autocorrelation:
ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))
= Cov(r100, r99) / (σ(r100) * σ(r99))
= Cov(-0.01, 0.02) / (σ(r100) * σ(r99))
Lag-2 Autocorrelation:
ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))
= Cov(r100, r98) / (σ(r100) * σ(r98))
To compute the 1- and 2-step-ahead forecasts of the return series at
t = 100, we use the given model:
1-step ahead forecast:
E(rt+1 | r100, r99) = E(0.02 + 0.5rt-1 + et+1 | r100, r99)
= 0.02 + 0.5r100
2-step ahead forecast:
E(rt+2 | r100, r99) = E(0.02 + 0.5rt | r100, r99)
= 0.02 + 0.5E(rt | r100, r99)
= 0.02 + 0.5(0.02 + 0.5r100)
The associated standard deviation of the forecast errors can be calculated as the square root of the variance of the return series, which is given as 0.02.
Thus,
Mean of rt = 0.02,
Variance of rt = 0.02,
Lag-1 Autocorrelation (ρ1) = -0.01,
Lag-2 Autocorrelation (ρ2) = Unknown,
1-step ahead forecast = -0.005,
2-step ahead forecast = 0.02,
The standard deviation of forecast errors = √0.02.
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(07.01)How many solutions can be found for the equation 4x = 4x?
O Zero
O One
Two
Infinitely many
Answers
Answer:
Infinitely many
Brainliest?
which of the following is not a survey mode mentioned in the text?a.person-administered.bputer-administered.c.self-administered.d.mixed-mode.
Answers
The survey mode that is not mentioned in the text is "puter-administered." The correct option is b: puter-administered.
The following is not a survey mode mentioned in the text: a.person-administered. b: puter-administered. c.self-administered. d.mixed-mode.
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what is the y-intercept of f(x)=5 x (1/6x)
Answers
Answer:
(5, 0)
Step-by-step explanation:
Answer:
(5 ,0)
I just turned it in and it was correct
Step-by-step explanation:
PLEASE MARK BRAINLIEST
The parallelogram shown represents a map of the boundaries of a natural preserve. Walking trails run from points A to C and from points B to D. The measurements shown represent miles. Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E. The length of D E is y + 2, the length of E B is 3 y minus 4, and the length of E C is 2 y minus 3. What is the sum of the lengths of the two trails? 6 miles 12 miles 16 miles 36 miles
Answers
Answer:
\(16\ \text{miles}\)
Step-by-step explanation:
In a parallelogram the diagnols bisect each other. So,
\(DE=EB\\\Rightarrow y+2=3y-4\\\Rightarrow 4+2=3y-y\\\Rightarrow 6=2y\\\Rightarrow y=\dfrac{6}{2}\\\Rightarrow y=3\)
\(DE=y+2\\\Rightarrow DE=3+2\\\Rightarrow DE=5\)
\(BD=2DE\\\Rightarrow BD=2\times 5\\\Rightarrow BD=10\)
\(EC=2y-3\\\Rightarrow EC=2\times 3-3\\\Rightarrow EC=3\)
\(AC=2EC\\\Rightarrow AC=2\times 3\\\Rightarrow AC=6\)
The sum of the diagonals is \(BD+AC=10+6=16\ \text{miles}\)
The sum of the lengths of the two trails is \(16\ \text{miles}\).
Answer:
16 Miles
Step-by-step explanation:
Just took the quiz and got it right
Help Please!!!!! (Look at picture
Answers
There is a number x such that x^3 is irrational and x^5 is rational justify
Answers
There exists a number x (specifically, the cube root of a non-perfect cube rational number) such that x³ is irrational and x⁵ is rational.
To justify the statement "there is a number x such that x³ is irrational and x⁵ is rational," we can use the fact that the product of a rational number and an irrational number is always irrational.
Let's assume that x is a rational number. Then, since any rational number raised to an odd power will remain rational, x³ and x⁵ would both be rational numbers. This would contradict our statement that x³ is irrational.
Therefore, x must be an irrational number. Now, let's consider the product x³ × x² = x⁵. Since x³ is irrational and x² is rational (since any real number raised to the power of 2 is always non-negative and therefore rational), the product x⁵ must be irrational.
However, we are looking for a number x such that x³ is irrational AND x⁵ is rational. To satisfy this, we can take x to be the cube root of a rational number that is NOT a perfect cube (i.e. not the cube of any rational number). This way, x³ will be irrational since it is the cube root of a non-perfect cube rational number.
Then, x⁵ = (x³) × (x²) will be rational since x³ is irrational and x² is rational.
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can some one help me plzz!! No links!!
Answers
if A={1,2,3}, find the relation in A×S satisfying the condition x+y<5.
Answers
Answer: This is copied from the internet:
Step-by-step explanation:
Answer:
For function, every element of the domain must have a unique image in co-domain...
(A)Let us redefine each function as a set of ordered pairs
and see if they satisfy the above condition (A) of a function f1={(1,2),(2,3),(3,4)} ; (4,5) cannot be an ordered pair as 5 does not belong to co-domain , Thus the element 4 of domain does not have an image.
f2={(1,4),(2,3),(2,4),(3,2)(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}
The uniqueness is violated as the elements have not one but many images.
f3={(2,1),(3,2),(3,1),(4,1),(4,2),(4,3)} Not a function as in f2 uniqueness is violated.
f4={(1,4),(2,3),(3,2)(4,1)} It is a function as each element has a unique image.
Help me please ive been on this zearn lesson for like 5 weeks and i still cannot past this please help. Question: This shape is made up of one half-circle attached to a square with side lengths 25 inches. You can use 3.14 as an approximation for π.
Answers
Answer:b
Step-by-step explanation:
Suppose there were m married couples, but that d of these 2m. people have died, Regard the d deaths as striking the 2m people at random. Let X be the number of surviving couples. Find:
Answers
The function that represents surviving people are X = 2m - d
Given that there are m married couples and d of the 2m of these couples have died, the total people that remain is expressed as:
Total people remaining = Total married couple - those that died
Total married couple = 2m
Total people that died = d
Taking the difference to get the remaining people;
Total people remaining = 2m - d
Hence the function that represents surviving people are X = 2m - d
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4-5 Isosceles and Equilateral Triangles
What is the value of x?
(5x)°
-(3x + 28)°
Answers
Answer:
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helppppppp meeeeeee I neep dajschelpbasbdb
what is 4x5x10
I wove humans
Answers
Answer:
200
Step-by-step explanation:
4 x 5 x 10
Multiply from left to right
4 x 5 x 10
20 x 10
200
Answer:
200
Step-by-step explanation:
Evaluate 6 – 2(a – b) when a = 4 and b = 2.
Answers
Answer:
2
Step-by-step explanation:
he school store is running a promotion on school supplies. Different supplies are placed on two shelves.
You can purchase 3 items from shelf A and 2 from shelf B for $26, or
You can purchase 2 items from shelf A and 5 from shelf B for $32.
Let x represent the cost of an item from shelf A and let y represent the cost of an item from shelf B. Write and solve a system of equations to find the cost of items from shelf A and shelf B. Show your work and thinking!
Answers
Answer:
Shelf A = $6 ;Shelf y = $4
Step-by-step explanation:
Let :
x = cost of items from shelf A
y = cost of items from shelf B
3x + 2y = 26 - - - - (1)
2x + 5y = 32 - - - - (11)
Using elimination method :
Multiply (1) by 2 and (11) by 3
6x + 4y = 52 - - - (111)
6x + 15y = 96 - - - (1V)
Subtract (1V) from (111)
-11y = - 44
y = 44/ 11 ; y = 4
Put y = 4 in (1)
3x + 2(4) = 26
3x + 8 = 26
3x = 26 - 8
3x = 18
x = 18 / 3
x = 6
You can use those variables specified to make symbolic relation between the cost and number of items. Then you can use any of the methods to solve the obtained system of equations.
The cost of items from shelf A is x = $6
The cost of items from shelf B is y = $4
Given that:
You can purchase 3 items from shelf A and 2 from shelf B for $26, orYou can purchase 2 items from shelf A and 5 from shelf B for $32.x represents the cost of an item from shelf A
y represents the cost of an item from shelf B
How to form the symbolic relation or equation between the cost and the number of items picked from each shelf?From given data, we have:
\(3 \times x + 2 \times y = \$26\\ 2 \times x + 5 \times y = \$32\)
Or, we get the system of equations as:
\(3x + 2y =26\\ 2x + 5y = 32\)
Using the method of substitution to deduce the solution:\(3x + 2y = 26\\ 2y = 26 - 3x\\ y = \dfrac{26-3x}{2} = 13 - 1.5x\)
Substituting this value of y in second equation, we get:
\(2x + 5y = 32\\ 2x + 5(13-1.5x) = 32\\ 2x - 7.5x + 65 = 32\\ -5.5x = -65 + 32\\ 5.5x = 33\\\\ x = \dfrac{33}{5.5}\\\\ x = 6\)
Using this value of x, we get:
\(y = 13 - 1.5x\\ y =13 - 1.5 \times 6\\ y = 13 - 9 = 4\)
Thus, we have:
The cost of items from shelf A is x = $6
The cost of items from shelf B is y = $4
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Akilah got a box of 24 assorted chocolates as a gift. The box contains 14 milk chocolates, 7 dark chocolates, and 3 toffees, but they are all individually wrapped so she doesn't know which candy is which kind. Dark Chocolate is Akilah's favorite. If she eats 2 candies today, what is the probability that... a) Both of the candies are dark chocolate? b) Neither of the candies are dark chocolate? c) at least one of the candies is dark chocolate? For all of the above, round to three decimal places. Question Help:
Answers
a) The probability that both candies are dark chocolate is 0.091. b) The probability that neither of the candies is dark chocolate is 0.495. c) The probability that at least one of the candies is dark chocolate is 0.505.
To solve these probability problems, we'll use the concept of combinations. The total number of candies in the box is 14 milk chocolates + 7 dark chocolates + 3 toffees = 24 candies.
a) Both candies are dark chocolate:
The probability of choosing a dark chocolate on the first draw is 7/24. After the first candy is drawn, there are 6 dark chocolates left out of 23 candies in the box. Therefore, the probability of choosing a dark chocolate on the second draw is 6/23.
To find the probability of both events occurring, we multiply the probabilities together:
P(Both dark chocolates) = (7/24) * (6/23) = 0.091 (rounded to three decimal places).
b) Neither of the candies are dark chocolate:
The probability of not choosing a dark chocolate on the first draw is 1 - 7/24 = 17/24. After the first candy is drawn, there are 16 non-dark chocolates left out of 23 candies in the box. Therefore, the probability of not choosing a dark chocolate on the second draw is 16/23.
To find the probability of both events occurring, we multiply the probabilities together:
P(Neither dark chocolate) = (17/24) * (16/23) = 0.495 (rounded to three decimal places).
c) At least one of the candies is dark chocolate:
To find the probability of at least one dark chocolate, we'll find the complement of the probability that neither of the candies is dark chocolate.
P(At least one dark chocolate) = 1 - P(Neither dark chocolate) = 1 - 0.495 = 0.505 (rounded to three decimal places).
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Brody has a jar with 1000 g of sugar in it. Each day, he empties out half
of the sugar that is in the jar. At the end of the first day, he is left with
500 g of sugar.
a) How much sugar will be left in the jar at the end of the 5th day? Give
your answer in grams (g).
b) Write a sentence to explain whether or not the jar will ever be empty
Answers
31.25 g on the 5th day
no it will never by empty because even when it gets down to one singular piece of sugar you would technically just cut it in half, then that in half, yes it would get impossible, that's why you wouldn't actually do it, but if you typed it into a calculator it would just keep getting a smaller and smaller decimal.
. Describe how to get the mixed number answer to 19÷6 from the
whole-number-with-remainder
answer. By considering a simple word problem, explain why the
method you describe makes
sense."
Answers
To obtain the mixed number answer to 19 ÷ 6 from the whole-number-with-remainder answer, divide the numerator (19) by the denominator (6).
To find the mixed number answer to 19 ÷ 6, we divide 19 by 6. The whole-number quotient is obtained by dividing the numerator (19) by the denominator (6), which in this case is 3. This represents the whole number part of the mixed number answer, indicating how many complete groups of 6 are in 19. Next, we consider the remainder. The remainder is the difference between the dividend (19) and the product of the whole number quotient (3) and the divisor (6), which is 1. The remainder, 1, becomes the numerator of the fractional part of the mixed number.
This method makes sense because it aligns with the division process and provides a clear representation of the result. It shows the whole number part as the number of complete groups and the fractional part as the remaining portion. This representation is helpful in various real-world scenarios, such as dividing objects or quantities into equal groups or sharing items among a certain number of people.
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