True or false: (a) If A2 is defined then A is necessarily square. (b) If AB and BA are defined then A and Bare square. (c) If AB and BA are defined then AB and BA are square. (d) If AB

Answers

Answer 1

(a) True. Suppose A is a not a square matrix, with m rows and n columns. Then A² is not defined, because you can't multiply an m×n matrix by another m×n matrix.

(b) False. As an example, consider the matrices

[tex]A_{3\times2} = \begin{bmatrix}1&0\\0&1\\0&0\end{bmatrix}[/tex]

[tex]B_{2\times3} = \begin{bmatrix}-1&0&1\\0&0&1\end{bmatrix}[/tex]

Then both AB and BA are defined, with

[tex]AB_{3\times3} = \begin{bmatrix}-1&0&1\\0&0&1\\0&0&0\end{bmatrix}[/tex]

[tex]BA_{2\times2} = \begin{bmatrix}-1&0\\0&0\end{bmatrix}[/tex]

In general, you can multiply any m×n by any n×m matrix.

(c) True. Multiplying a m×n matrix by a n×m matrix always yields a m×m matrix, and multiplying a n×m matrix by a m×n matrix always yields a n×n matrix.


Related Questions

What is 4 divided by 1/8

Answers

4 divided by 1/8 is 32

Hello.

First, let's convert 4 into a fraction.

Here's how we do it:

[tex]\mathrm{4=\displaystyle\frac{4}{1} }[/tex]

Now, what is [tex]\displaystyle\frac{4}{1}[/tex] divided by [tex]\displaystyle\frac{1}{8}[/tex]?

In order to figure that out, we need to flop the second fraction over:

[tex]\displaystyle\frac{4}{1} : \frac{8}{1}[/tex]

Now, multiply:

[tex]\mathrm{\displaystyle\frac{4}{1} *\frac{8}{1} }[/tex]

[tex]\mathrm{\displaystyle\frac{32}{1} }[/tex]

[tex]\mathrm{32}[/tex]

Therefore, the final answer is [tex]\mathrm{32}[/tex].

I hope this helps.

Have a nice day.

[tex]\boxed{imperturbability}[/tex]

Solve the system of equations:
X+y+z=5
-3x-4y+4z=15
2x-y-4z=-8

Answers

Answer:

Solution By Gauss jordan elimination method

x = 3, y = 2 and z = 4

help asap will mark brainliest to the correct answer and 5 star it

Answers

Answer:

50°

Step-by-step explanation:

The missing angle would equal the formula:

180°- a - b= x

a and b are the two angles given.

180- 110 -20 = 50

So the missing angle is 50 °

Choose the property that is displayed the equation below: (a + b).c= c.(a + b) a+b​

Answers

Answer:

I think maybe associative property of addition?

What is the quotient? PLEASE HELP QUICK

Answers

Answer:

[tex]\frac{1}{5^{9} }[/tex]

Step-by-step explanation:

[tex]\frac{5^{-6} }{5^{3} }[/tex]

Rewrite [tex]5^{3}[/tex] as [tex]5^{-6}[/tex] × [tex]5^{9}[/tex]. Cancel out [tex]5^{-6}[/tex] in both numerator and denominator.

= [tex]\frac{1}{5^{9} }[/tex]

Hope it helps and have a great day! =D

~sunshine~

Answer:

[tex]\mathrm{The\:first\:option}:\quad\dfrac{ 1 }{ { 5 }^{ 9 } }[/tex]

Step-by-step explanation:

[tex]\dfrac{ { 5 }^{ -6 } }{ { 5 }^{ 3 } }[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \dfrac{ { x }^{ a } }{ { x }^{ b } } = { x }^{ a-b }[/tex]

[tex]= { 5 }^{ -6-3 }[/tex]

[tex]\mathrm{Subtract\:the\:numbers:}\:-6-3=-9[/tex]

[tex]=5^{-9}[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \:{ a }^{ -b } = \dfrac{ 1 }{ { a }^{ b } }[/tex]

[tex]\dfrac{ 1 }{ { 5 }^{ 9 } }[/tex]

So the correct answer would be:

[tex]\mathrm{The\:first\:option}:\quad\dfrac{ 1 }{ { 5 }^{ 9 } }[/tex]

   

A quantity with an initial value of 3700 decays exponentially at a rate of 6% every 5
minutes. What is the value of the quantity after 36 minutes, to the nearest
hundredth?

Answers

Answer:

2369.86

Step-by-step explanation:

f(36)=3700(1−0.06) ^36/5

2369.857704098921

The value of the quantity after 36 minutes is approximately 3701.5.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for exponential decay to find the value of the quantity after 36 minutes:

[tex]A =A_{0} e^-^r^t[/tex]

where:

A₀ = initial value = 3700

r = decay rate per unit time = 6% = 0.06

t = time in minutes

We want to find A after 36 minutes, so:

t = 36

Substituting these values into the formula, we get:

[tex]A = 3700e^(^-^0^.^0^6^\times^ 3^6^/^5)[/tex]

A=3701.5

Therefore, the value of the quantity after 36 minutes is approximately 3701.5.

To learn more on Percentage click:

https://brainly.com/question/28269290

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The numbers 38 and 41 are rounded to the nearest ten and then multiplied to estimate the product. What is the best estimate of 38 × 41 based on this method?

1,200
1,600
2,000
2,500


The numbers 38 and 41 are rounded to the nearest ten and then multiplied to estimate the product. What is the best estimate of 38 × 41 based on this method?

1,200
1,600
2,000
2,500




What is the product of 21 × 3?

21
24
60
63




Yusef wants to buy 20 pairs of sneakers to donate to a local shelter. Each pair costs $23. How much money will Yusef spend on all the sneakers?

$100
$200
$360
$460




The product of 42 × 31 is
.

A basketball team has 22 games this season. At each game, 95 raffle tickets are sold. How many raffle tickets are sold during all 22 games?

1,900
1,980
2,080
2,090



Carter rewrites 28 × 2 in expanded form to find the product.

28 × 2

= (20 × 2) + (8 × 2)

What is the next step to find the product?

adding the product of 20 × 2 to the product of 8 × 2
subtracting the product of 20 × 2 from the product of
8 × 2
multiplying the product of 20 × 2 by the product of 8 × 2
dividing the product of 20 × 2 by the product of 8 × 2



What is the product of 33 × 2?

31
33
60
66





What is the product?

57 × 4

228
232
240
285




Marta has 128 stamps. Kelli has 11 times as many as Marta. Marta estimates the total they have altogether by rounding each amount to the nearest ten and then multiplying.

What is the best estimate of 128 × 11 using this method?

1,200
1,300
1,408
1,508

pls hurry first one right gets brainlist

Answers

Answer:

Jeez this is a big question

Step-by-step explanation:

1. if they are rounded to the nearest 10 that would mean that it is actually

40 * 40

40 * 40 is 1600. The answer for #1 is 1600

2. its just asking what 21 x3 is, 21x3 is 63

3. All you do for this is 20*23

20 * 23 is 460

4. 42 * 31 is 1302

5. 22 * 95 = 2090

6. You do 20x2 which is 40 and then you do 8x2 which is 16

Adding

then you have 40 + 16 = 56

Subtracting

40 - 16 = 24

Multiplying

40 * 16 = 640

Dividing

40/16 = 2.5

7. 33x2 is 66

8. 57* 4 is 228

9. 128 * 11 is 1408 but if you round the 11 to the nearest 10, that would be 10, then if you round the 128 to the nearest 10, that would be 130, and then 130 * 10 is 1300

38 × 41 can be estimated by rounding 38 and 41 to the nearest ten, which gives us 40 and 40. Multiplying these two numbers gives us 1600. So the answer is 1,600.

21 × 3 is equal to 63.

How to solve

Yusef wants to buy 20 pairs of sneakers to donate to a local shelter. Each pair costs $23. How much money will Yusef spend on all the sneakers? The answer is $460.

The product of 42 × 31 is 1,262.

A basketball team has 22 games this season. At each game, 95 raffle tickets are sold. How many raffle tickets are sold during all 22 games? The answer is 2,090.

Carter rewrites 28 × 2 in expanded form to find the product.

28 × 2

= (20 × 2) + (8 × 2)

The next step to find the product is to multiply the product of 20 × 2 by the product of 8 × 2.

= 20 × 2 + 8 × 2

= 40 + 16

= 56

What is the product of 33 × 2? The answer is 66.

What is the product?

57 × 4

= 228

Marta has 128 stamps. Kelli has 11 times as many as Marta. Marta estimates the total they have altogether by rounding each amount to the nearest ten and then multiplying.

What is the best estimate of 128 × 11 using this method? The answer is 1,300.

Read more about algebra here:

https://brainly.com/question/22399890

#SPJ3

How many times greater is one gallon than one quart. PLEASE HELP ME

Answers

Answer:

4 quarts constitute for 1 gallon.

Let's convert quarts into gallon.

Explanation: A quart contains 4 cups or 2 pints while a gallon contains 16 cups or 8 pints. Hence, a liquid gallon is equal to 4 liquid quarts.

Step-by-step explanation:

[tex]hope \: it \: helps \: you[/tex]

Frank has $156.87 he spends $21.58 to buy a gift for his sister he also earned $45.50 how much does he have now?

Answers

Answer:

$89.79

Step-by-step explanation:

156.87-21.58-45.5 = $89.79

The angles of a triangle are in a ratio 1:3:8. What are the angles?

Answers

Answer:

15° , 45°, 120°

Step-by-step explanation:

sum the parts of the ratio, 1 + 3 + 8 = 12 parts

the sum of the 3 angles in a triangle = 180° , then

180° ÷ 12 = 15° ← value of 1 part of the ratio, then

3 parts = 3 × 15° = 45°

8 parts = 8 × 15° = 120°

the 3 angles are 15° , 45° , 120°

Write and graph an equation that represents the total cost in dollars) of renting the bounce house. Let H represent number of hours and C represent the total cost in dollars) of the rental.
How much does it cost to rent the bouncy house for 6 hours?

Answers

Answer:

C= $25 x 6 = $150

Step-by-step explanation:

HELP ME I WILL GIVE BRINLEST

Answers

Answer:

9 and 1 fourths

Step-by-step explanation:

Answer:

10 9/16

Step-by-step explanation:

For this equation, we are going to need to multiply these mixed numbers to get our answer. The quickest and easiest way to solve this would be to turn these mixed numbers into improper fractions.

(Important:) To make an improper fraction, multiply the denominator by the whole number, then add the numerator. This becomes your new numerator for your improper fraction.

With that said, we can now turn these into improper fractions. So:

3 1/4 = 13/4 and 13/4.

To find area, we need to multiply L x W (length x width) to get our answer. So:

13/4 x 13/4 = 169/16 = 10 9/16.

I hope that this helps.

Write an equation based on the graph.

Answers

Y=(-2/3x)+2

You don’t have to include the parentheses. I just placed them there so you know that it’s -2 over 3x plus 2

write an equation for line in slope intercept form ?

Answers

Step-by-step explanation:

the standard slope-intercept form is

y = ax + b

the factor of x (here "a") is always the slope of the line. b is the y-intercept (the y value when x = 0).

the slope of the other line is 5/6.

ok.

perpendicular to this means in a right angle (90°).

and that means that the fraction of "y coordinate change / x coordinate change" turns upside-down, and the sign has to flip.

so, the slope of our line is then -6/5.

and b ?

we use the given point.

1 = -6/5 × -9 + b = 54/5 + b

5/5 = 54/5 + b

b = -49/5

and our line equation is

y = (-6/5)x - 49/5

Write 425% as a fraction or mixed number in simplest form.

Answers

Answer:

17/40

here! hope this helps!

Jenny randomly selects 20 boxes of crayons from the shelf and finds two boxes with at least one broken crayon. If the shelf holds 130 boxes, how many would you expect to have at least one broken crayon?

Answers

13 crayons she would expect to be broken

I WILL GIVE BRAINLEST

Answers

[tex] \huge{ \rm{Question:}}[/tex]

7. If a figure measures 7 centimeters high, 3 centimeters wide and 2 centimeters deep, what is the volume of the figure?

[tex] \huge{ \rm{Answer:}}[/tex]

The volume of the figure is 42.

Step-by-step explanation:

= 2 x 7 x 3

= 14 x 3

= 42

HOPE THIS HELPS^^

the volume would be 42

what is the 40th term of the arithmetic sequence 13, 26, 39, 52

Answers

Answer:

your answer would be 520

Step-by-step explanation:

13 x 40 = 520

Deon set a goal to ride his bicycle
310 miles in a month. He has biked
145 miles so far. If there are 4 days left
in the month, about how many miles
should Deon ride each day to reach his
goal? Explain.

Answers

Answer:

it could be 42.25

Step-by-step explanation:

I know this because 310-145=165/4=42.25

(you MIGHT need to round it)

1.) 10 + 8 ÷ 2 ( 4 + 3 )



2.) 21 ÷ ( 1 ) ( 3 ) + 0 - 14

Answers

Answer:

1) 38

2) 49

Step-by-step explanation:

1) 10 + 8 ÷2(4 + 3)

Knowing Pemdas, we do the expression in the parentheses first.

4+3 = 7

The new expression is: 10 + 8 ÷ 2 · 7

Using Pemdas, 8 ÷ 2 is 4.

10 + 4 · 7

10 + 28 = 38.

The answer to #1 is 38.

2)  21 ÷ ( 1 ) ( 3 ) + 0 - 14

21 ÷ 1 = 21

21 · 3 = 63

63 + 0 = 63

63 - 14 = 49

The answer to #2 is 49.

The bookshelf is 6 feet tall how many yards is the bookshelf

Answers

Answer:

1 yard is equal to 3 feet

6 feet(total)

___________ = 2 yards

3 feet(equal to one yard)

The graph to the left shows the cost, in dollars, of gasoline per gallon of gas.
Cost of Gasoline
Select ALL of the statements which are correct.

Answers

Answer:

correct statements are #1,3,5

Step-by-step explanation:

second check box represents the cost of 7 gallons

fourth check box is incorrect because the unit price of gas is 3 dollars for each gallon

Can someone help please

Answers

Answer:

1=1/2

2=8 times the square root of 3 over 25     8xsuare root 3/25

3=16

4=7 times square root of 3 over 4    7x square root 3/4

5=square root of 2 over 2

6=square root 3

7=square root 2

8=1/3

9=10/7

Step-by-step explanation:

you can also use algebrator square root calculator!!

Help me please please

Answers

Answer: 2052

Step-by-step explanation: 684 times 3 equal to 2052

The three angles of a triangle are presented as the
monomials 4x,6x, and 2x. Find the measure of each angle
and then classify the triangle accordingly.

Answers

Answer:

Step-by-step explanation:

4x+6x+2x=180

12 x=180

x=180/12=15

angles are 4×15=60°,6x=6×15=90°,2x=2×15=30°

so angles are 60°,90°,30°

it is a right angled triangle.

In a village 200 persons out of 450 were found to be alcoholic. Can you conclude that minority of persons in this village are alcoholic assuming the persons being alcoholic and non-alcoholic are equal?​

Answers

Step-by-step explanation:

Step 1 total number of person =450

Step 2 number of people who are alcholic =200

Step 3 now subtract them like: 450 - 200

Answer=200 people are non alcholic


1. The area of a circle is 60 square units. What is the area of ...
of the circle.
50% of the circle

Answers

Multiply the area of the circle by the percentage:

60 square units x 50% = 60 x 0.50 = 30

50% 0f the circle id 30 square units.

What is the slope and y-intercept? 20 points!!

Answers

Answer:

Slope: 1/2

Y-int: -4

[tex]\tt slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

point 1 = -1,-6

point 2 = 0,-4

slope:

[tex]\tt \dfrac{-4+6}{0+1}=2[/tex]

y intercept when x = 0, so y intercept from table = -4

what is the value of F

Answers

Answer:

-15

Step-by-step explanation:

If a book and a pen together cost $11 and the book is $10 more than the pen, how much does the pen cost? Show solution please

Answers

Answer:

50 cents

Step-by-step explanation:

Since 1 dollar is too much, then try 50 cents. Then it worked.

x+y=z
10+1=11
this is the solution
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