True/False Questions: For statements that are true, give a very short expla- nation. For statements that are false, give an example. (a) If A is an invertible matrix, then A is an invertible matrix. (b) If A is an invertible matrix, then A+ A is an invertible matrix. (c) If A and B are n x n matrices, such that AB is invertible, then it follows that B is invertible. (d) If A and B are n x n invertible matrices, then it follows that A - B must be an invertible matrix.
Answers
(a) If A is an invertible matrix, then A is an invertible matrix. - True
Explanation:
If A is invertible, then A has an inverse matrix A^(-1).
(b) If A is an invertible matrix, then A+ A is an invertible matrix. - False
Explanation:
A+ A = 2A is invertible if and only if A is invertible.
Therefore, this statement is false.
(c)
If A and B are n x n matrices, such that AB is invertible, then it follows that B is invertible. - False
Explanation:
Even if AB is invertible, it is not always true that B is invertible.
For instance, if A = [1 0], B = [0 1],
then AB = [0 1] which is invertible, but B is not invertible.
(d)
If A and B are n x n invertible matrices, then it follows that A - B must be an invertible matrix. - False
Explanation:
If A = [2 0], B = [0 1], then both A and B are invertible, but A - B = [2 -1] is not invertible.
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Related Questions
Please help quick what is the area of the shaded region
Answers
Answer:
370 mm sq
Step-by-step explanation:
bxh/2=area of triangle
so 20/2x37=370
A box shaped like a rectangular prism has a length of 8 inches and width of 8 inches. Its volume is 512 cubic inches. What is the height of the box?
Answers
Answer:
8 inches
Step-by-step explanation
the volume is length x width x height
so the equation would be 8 x 8 x (height) = 512
8x8 is 64, and you divide 512 by 64 which is 8
Solve the following inequality:
-2(-4/5x+3)-x=3x
Answers
Answer:
x= -5/2
Step-by-step explanation:
First distribute -2 to all the numbers in the parenthesis.
8/5x-6-x=3x
8/5/4=
2/5-6
=-5/2
Hope this helps!
The base of an empty rectangular tank measures 50cm by 40cm. The tank is gilled with water up to 1/4 of its height. The volume of the water in the tank is 52L. What is the height of the tank?
Answers
Answer:
height of tank = 104 cm
Step-by-step explanation:
the volume (V) of a rectangular tank is
V = Ah ( A is the area of the base and h the height )
here A = 50 × 40 = 2000 cm²
all units must be the same, so
note that 1 litre = 1000 cm³
then 52L = 52 × 1000 = 52000 cm³
height of water in tank is then
2000h = 52000 ( divide both sides by 2000 )
h = 26 cm
this h is \(\frac{1}{4}\) of the height of the tank, thus
height of tank = 4 × 26 cm = 104 cm
Mrs. Bosch's science club left the school on a bus at 7:48 a.m. to go to Orlando. Mrs. Bosch drove her own car and did not leave the school until 8:40 a.m. The bus traveled at an average rate of 80 kilometers per hour. What was Mrs. Bosch's average speed, to the nearest kilometer per hour, if she met up with the bus when they stopped for lunch at 1:00 p.m.?
Answers
Please help with these questions a b and c pls tyyyyyyy
Answers
Answer:
23, 5, 3
Step-by-step explanation:
Following the order of operations as stated in PEMDAS , then
(a)
5 + 2 × 3² ← evaluate exponent
= 5 + 2 × 9 ← perform multiplication
= 5 + 18 ← perform addition
= 23
---------------------------------------
(b)
\(\frac{7+8}{5-2}\) ← perform calculations on numerator/denominator
= \(\frac{15}{3}\) ← perform division
= 5
-------------------------------------------
(c)
\(\frac{18-3(2)}{5-1^2}\) ← evaluate numerator/denominator using PEMDAS
= \(\frac{18-6}{5-1}\)
= \(\frac{12}{4}\)
= 3
40 x 7 = _________ x 10 x 7
Answers
40 x 7 = _________ x 10 x 7
280 = ? x 70
280 = 4 x 70
check: 280 = 280
4 goes in the blank
Answer:
4
Step-by-step explanation:
40×7=280
10×7=70
280:70=4
what is this means and what is the answer 2x*2x
Answers
Answer: 4x^2
Step-by-step explanation:
Sorry I don't know how to explain I hope this helps you have a great day
If m angle ABF =8w-6 and m angle ABE = 2(w + 11) find m angle EBF
Answers
Answer:
Angle EBF = 6w -28
Step-by-step explanation:
Given:
ABF = 8w - 6
ABE = 2(w + 11)
Find:
Angle EBF
Computation:
Angle EBF = ABF - ABE
Angle EBF = 8w - 6 - [2(w + 11)]
Angle EBF = 8w - 6 - [2w + 22]
Angle EBF = 8w - 6 - 2w - 22
Angle EBF = 6w -28
The value of the angle EBF will be 6w -28.
What is an angle?The vertex of the angle is the angle's shared terminal. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
These are called dihedral angles. The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Given that angle ABF =8w-6 and m angle ABE = 2(w + 11). The value of the angle EBF will be calculated as:-
Angle EBF = ABF - ABE
Angle EBF = 8w - 6 - [2(w + 11)]
Angle EBF = 8w - 6 - [2w + 22]
Angle EBF = 8w - 6 - 2w - 22
Angle EBF = 6w -28
Therefore, the value of the angle EBF will be 6w -28.
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Which of these sets have the integers in order
from least to greatest?
-42, -32, -39, -10
-42, -39, -32,-10
-10,-32, -39,-42
-10, -39, -32, -42
Answers
Answer:
-10,-32, -39,-42
Step-by-step explanation:
-10,-32, -39,-42
1.21 is 42% of what number?
(1 Point)
8.82
50
200
Answers
50%
200%
That is my answer hoped it helped
Compare the values.
9 x 10^2 is
?
times as much as 3 x 10^-2.
Answers
Answer:
Hopefully this explains o_O, also Merry Christmas!
Step-by-step explanation:
9 x 10^2 = 9 x 100 = 900
3 x 10^-2 = 3 x 1/100 = 0.03
Ratio of 900:0.03
The first one is 30000 bigger than the second
3 x 10^-2 = 0.03
30000 times more
900 : 0.03 = 30000
Put these fractions in order from least to greatest 7/10 4/5 1/2
Answers
Answer:
1/2, 7/10, 4/5
Step-by-step explanation:
the chance of getting a rare disease is .03 per person. out of 1,000 people, how many of them are expected to get the disease?
Answers
Answer:
I believe the answer would be 30 people.
Step-by-step explanation:
To calculate the percentage out of a group of people or items, you just multiply the percent (in decimal form) by the amount of people you want it out of. For example: A 0.1% chance out of 1,000 people would be a chance and expectancy of 1 person out of those 1,000 people. In this case it's 3% for every person. 0.03 • 1,000 is 30.
For the following exercise determine whether the graph shown represents a geometric sequence.
Answers
Answer:
Graph of a geometric sequence
equal changes in the input cause the output to be successively multiplied by a constant. cause the output to be successively multiplied by a constant (determined by the common ratio). Thus, geometric sequences always graph as points along the graph of an exponential function.
An example of a geometric sequence is given below as
A geometric sequence takes the function given in the formula below
\(a_n=ar^{n-1}\)When n=1, An=-3
\(\begin{gathered} a_{n}=ar^{n-1} \\ -3=ar^{1-1} \\ -3=a \\ a=-3 \end{gathered}\)When n=2 ,An=-1
\(\begin{gathered} a_{n}=ar^{n-1} \\ -1=-3r^{2-1} \\ -1=-3r \\ r=\frac{-1}{-3} \\ r=\frac{1}{3} \end{gathered}\)When n=3,An =1
\(\begin{gathered} a_{n}=ar^{n-1} \\ 1=3r^{3-1} \\ \frac{1}{3}=r^2 \\ r^=\sqrt{\frac{1}{3}} \end{gathered}\)We can see that they do not have a constant value of the common ratio (r)
Hence,
The graph DOES NOT represent a geometric sequence
Write 45 as a product of three primes
Answers
Answer:
1, 3, 5
Step-by-step explanation:
:)
Answer:
3 x 3 x 5
Step-by-step explanation:
Prime numbers are numbers that cannot factor any lower then itself and one (which includes, but is not limited too: 1, 3, 5, 7, 11, 13, 17, etc.
5 x 1 = 5
3 x 1 = 3
Factor:
45 = 15 x 3
15 = 5 x 3
3 x 3 x 5 is your answer.
1. la altura 3 de un cohete viene dada por la expresión h(t) =50 t -5t ², donde t viene dando en segundos y h (t) en metros
a) que altura alcanza el cohete al cabo de 1,2 y 5 segundos
b)¿y al cabo de 10 s? como interpretas este ultimo resultado
Answers
Answer:
a)
h(1.2) =52.8
h(5)=125
b) h(10)=0 .Este valor es lo que tarda el cohete en tocar el suelo.
Step-by-step explanation:
Para contestar esta pregunta debemos reemplazar el valor de t (segundos) por los valores requeridos en la siguiente ecuación:
h(t) =50 t -5t ²
a)
h(1.2) =50 (1.2) -5(1.2)²
h(1.2) = 60-5(1.44)
h(1.2) = 60-7.2 = 52.8
h(5) =50 (5) -5(5)²
h(5) =250-5(25)
h(5)=250-125=125
b)
h(10) =50 (10) -5(10)²
h(10)= 500-5(100)
h(10) = 500-500=0
Este valor es lo que tarda el cohete en tocar el suelo, en 10 segundos la altura h es 0.
In the table, x represents minutes, and y represents the altitude of an airplane.
Altitude of an Airplane
Minutes, x
Altitude in feet, y
15
22,500
20
20,000
25
17,500
30
15,000
Which statement is correct about the slope of the linear function that the table represents?
The slope is positive because as the minutes decrease, the altitude increases.
The slope is positive because as the minutes increase, the altitude increases.
The slope is negative because as the minutes decrease, the altitude decreases.
The slope is negative because as the minutes increase, the altitude decreases.
Answers
Answer:
it is d i took the quiz
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
i took the quiz
elimination method -2x-7y=13 and 3x+6y=15
Answers
Answer:
The answer is (61/3), (-23/3)
Step-by-step explanation:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Hoped this helped!
I don’t understand ??
Answers
Answer:
10 is the answer because it makes the equation in the right bigger from the left equation for this u have to solve with all options and find which is bigger
Step-by-step explanation:
50 points if you answer correctly
Answers
Answer:
\(f(3) = {3}^{2} + 5(3) - 9 \\ f(3) = 9 + 15 - 9 \\ f(3) = 15\)
Answer:
1. D. 15
2. A. 3
3. A. c= 6g+5
4. A. All real numbers
5. D
\section*{Problem 2}
\subsection*{Part 1}
Which of the following arguments are valid? Explain your reasoning.\\
\begin{enumerate}[label=(\alph*)]
\item I have a student in my class who is getting an $A$. Therefore, John, a student in my class, is getting an $A$. \\\\
%Enter your answer below this comment line.
\\\\
\item Every Girl Scout who sells at least 30 boxes of cookies will get a prize. Suzy, a Girl Scout, got a prize. Therefore, Suzy sold at least 30 boxes of cookies.\\\\
%Enter your answer below this comment line.
\\\\
\end{enumerate}
\subsection*{Part 2}
Determine whether each argument is valid. If the argument is valid, give a proof using the laws of logic. If the argument is invalid, give values for the predicates $P$ and $Q$ over the domain ${a,\; b}$ that demonstrate the argument is invalid.\\
\begin{enumerate}[label=(\alph*)]
\item \[
\begin{array}{||c||}
\hline \hline
\exists x\, (P(x)\; \land \;Q(x) )\\
\\
\therefore \exists x\, Q(x)\; \land\; \exists x \,P(x) \\
\hline \hline
\end{array}
\]\\\\
%Enter your answer here.
\\\\
\item \[
\begin{array}{||c||}
\hline \hline
\forall x\, (P(x)\; \lor \;Q(x) )\\
\\
\therefore \forall x\, Q(x)\; \lor \; \forall x\, P(x) \\
\hline \hline
\end{array}
\]\\\\
%Enter your answer here.
\\\\
\end{enumerate}
\newpage
%--------------------------------------------------------------------------------------------------
Answers
The argument is invalid because just one student getting an A does not necessarily imply that every student gets an A in the class. There might be more students in the class who aren't getting an A.
Therefore, the argument is invalid. The argument is valid. Since Suzy received a prize and according to the statement in the argument, every girl scout who sells at least 30 boxes of cookies will get a prize, Suzy must have sold at least 30 boxes of cookies. Therefore, the argument is valid.
a. The argument is invalid. Let's consider the domain to be
\(${a,\; b}$\)
Let \($P(a)$\) be true,\($Q(a)$\) be false and \($Q(b)$\) be true.
Then, \($\exists x\, (P(x)\; \land \;Q(x))$\) is true because \($P(a) \land Q(a)$\) is true.
However, \($\exists x\, Q(x)\; \land\; \exists x \,P(x)$\) is false because \($\exists x\, Q(x)$\) is true and \($\exists x \,P(x)$\) is false.
Therefore, the argument is invalid.
b. The argument is invalid.
Let's consider the domain to be
\(${a,\; b}$\)
Let \($P(a)$\) be true and \($Q(b)$\)be true.
Then, \($\forall x\, (P(x)\; \lor \;Q(x) )$\) is true because \($P(a) \lor Q(a)$\) and \($P(b) \lor Q(b)$\) are true.
However, \($\forall x\, Q(x)\; \lor \; \forall x\, P(x)$\) is false because \($\forall x\, Q(x)$\) is false and \($\forall x\, P(x)$\) is false.
Therefore, the argument is invalid.
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At a concert, 20% of the people are wearing black dresses or suits, 1/4 are wearing navy, 0.35 are wearing brown, and the rest are wearing a variety of colors. (other). What percent are wearing “other”? Type in your answer using the decimal equivalent of this amount.
Answers
Answer: 20%
Step-by-step explanation:
20% black dresses or suits
.35 = 35% wearing brown
1/4 = 25% wearing navy
100% -20% - 35% - 25% = 20% left
the number of units expected to be sold is uniformly distributed between 300 and 500. if r is a random number between 0 and 1, then the proper expression for sales is
Answers
300 + (200)r is the proper expression for sales if the number of units expected to be sold is uniformly distributed between 300 and 500. If r is a random number between 0 and 1.
What is a random number?
a random number is a number chosen by chance -- i.e., randomly, from a set of numbers. All the numbers in a specified distribution have equal probability of being chosen randomly.
Given that r is a random number between 0 and 1. it is uniformly distributed between 300 and 500 will be done by using the formula of 300+200r.
If r = 0, 300+200r will result in the output as 300
If r = 0.5, 300+200r will result in the output as 400
If r= 1, 300+200r will result in the output as 500
Hence ,the proper expression for sales is 300+200r
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The cash-in receipts (money going in) in Brandon's cash drawer total $823.27, and his cash-out receipts (money leaving) total $734.87. If he currently has $338.40 in his drawer, how much money did he start with in the drawer?
Answers
Answer:
$250
Step-by-step explanation:
Let x = amount he started with in his drawer
x + $823.27 - $734.87 = $338.40
$823.27 would be added because it is money going in
$734.87 would be subtracted because it is the money going out
solve for x
x = $250
Arrange the steps to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm in the order. a = 2, m=17 Rank the options below. The ged in terms of 2 and 17 is written as 1 = 17-8.2. By using the Euclidean algorithm, 17 = 8.2 +1. The coefficient of 2 is same as 9 modulo 17. 9 is an inverse of 2 modulo 17. The Bézout coefficients of 17 and 2 are 1 and 8, respectively. a = 34, m= 89 Rank the options below. The steps to find ged(34,89) = 1 using the Euclidean algorithm is as follows. 89 = 2.34 + 21 34 = 21 + 13 21 = 13 + 8 13 = 8 + 5 8 = 5 + 3 5 = 3 + 2 3 = 2+1 Let 34s + 890= 1, where sis the inverse of 34 modulo 89. $=-34, so an inverse of 34 modulo 89 is -34, which can also be written as 55. The ged in terms of 34 and 89 is written as 1 = 3 - 2 = 3-(5-3) = 2.3-5 = 2. (8-5)- 5 = 2.8-3.5 = 2.8-3. (13-8)= 5.8-3.13 = 5. (21-13)-3.13 = 5.21-8. 13 = 5.21-8. (34-21) = 1321-8.34 = 13. (89-2.34) - 8.34 = 13.89-34. 34 a = 200, m= 1001 Rank the options below. By using the Euclidean algorithm, 1001 = 5.200 +1. Let 200s + 1001t= 1, where sis an inverse of 200 modulo 1001. The ged in terms of 1001 and 200 is written as 1 = 1001 - 5.200. s=-5, so an inverse of 200 modulo 1001 is -5.
Answers
We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).
How do we find the inverse of a modulus?To find the inverse of a module m using Euclid's algorithm, the steps are as follows:
1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.
2. Let a = GCD * s + m*t, where s is the inverse of a module m.
3. The GCD in terms of a and my is written as 1 = m-s*a.
4. Find s = -a, so the inverse of a module m is -a (or m+s).
For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).
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what is 28.5 inches in height?
Answers
determine if the given shapes are polygons or not if polygons name the classification according to sides
Answers
a ranking of athletes is an ordered list of their names with no repetitions. in other words, each athlete is given a rank between and , which corresponds to their position in the list. a tie is the situation where more than one athlete is given the same rank. how many ways are there to rank four athletes without any ties?
Answers
There are 24 ways to rank four athletes without any ties.
To calculate the number of ways to rank four athletes without any ties, we can use the concept of permutations. Since each athlete is given a distinct rank, we need to arrange them in a specific order.
The first athlete can be ranked in 4 different positions (1st, 2nd, 3rd, or 4th). After assigning a rank to the first athlete, the second athlete can be ranked in 3 remaining positions. Similarly, the third athlete can be ranked in 2 remaining positions, and the fourth athlete takes the remaining 1 position.
The total number of ways to rank four athletes without any ties is calculated as follows:
4 x 3 x 2 x 1 = 24
Therefore, there are 24 ways to rank four athletes without any ties.
When ranking four athletes without any ties, there are 24 possible arrangements. Each athlete is assigned a distinct rank, resulting in a total of 24 different ways to order the athletes.
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difer from the true proportion by more than 2% ? A previous study indicates that the proportion of lefthanded sclontists is 9%. Round up to the nearest whicie number. Duestion 13 A. 1.218 B. 1,109 C. 14 D.767
Answers
The total number of samples will be 1109 .
Given ,
Margin of error 0.02
Here,
According to the formula,
\(Z_{\alpha /2} \sqrt{pq/n}\)
Here,
p = proportions of scientist that are left handed
p = 0.09
n = number of sample to be taken
Substitute the values,
\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)
n ≈1109
Thus the number of samples to be taken will be approximately 1109 .
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