Let A and B be arbitrary matrices for which the indicated product is defined. Determine whether the statement below is true or false. Justify the answer. If A and B are 2 x 2 with column a1,a2 and b1, b2 respectivley then AB= [a1b1, a2b2]

Each column of AB is a linear combination of the columns of B using weights from the corresponding column of A.

a. True
b. False

Answers

Answer 1

Answer:

b. False

Step-by-step explanation:

Let A and B be matrices with the rows a1a2 and b1b2 respectively. Suppose the other two columns are c1,c2 and d1d2 having a value equal to zero.

A=   a1   c1                      B=  b1       d1

      a2  c2                            b2      d2

Multiplying

AXB= a1b1+c1b2         a1d1+c1d2

          a2b1+c2b2       a2d1+c2d2

AB=║ a1b1         0║

      ║a2b1        0 ║

Hence the given statement is false.

Each column of AB is a linear combination of the ROWS of A using weights from the corresponding column of B.

The matrix multiplication is "row by column" i.e the rows of the first matrix are multiplied with the columns of the second matrix.

The rows are also used in multiplication.


Related Questions

what value of x makes the equation true
-(8x+3)=-23-3x

Answers

Answer:

x = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/CoefficientsFactoring

Step-by-step explanation:

Step 1: Define

-(8x + 3) = -23 - 3x

Step 2: Solve for x

Factor GCF:                                                                                                       -(8x + 3) = -(23 + 3x)[Division Property of Equality] Divide -1 on both sides:                                 8x + 3 = 23 + 3x[Subtraction Property of Equality] Subtract 3x on both sides:                      5x + 3 = 23[Subtraction Property of Equality] Subtract 3 on both sides:                        5x = 20[Division Property of Equality] Divide 5 on both sides:                                  x = 4

What is the sum of the measures of the interior angles of a 20-sided figure?

Enter your answer in the box.

__°

Answers

The sum of the measures of the interior angles of a 20-sided figure is 3240.

What are Interior angles ?

An interior angle of a polygon is an angle that is created between two of the polygon's adjacent sides. The interior angle of a polygon is also known as the angle measured at the interior of a polygon.

the number of sides of given polygon is 20.

we know that, sum of the measures of the interior angles can be found by using formula : (n-2) × 180

where n= no. of sides of given polygon

So, sum of the measures of the interior angles of 20 sided figure :

     = (n-2) × 180

     = (20-2) × 180

     = 18 × 180

     = 3240 .

To learn more about Interior angles, visit the link :

https://brainly.com/question/24966296

#SPJ1

half the sum of 8 and r​

Answers

Ummm I need the full question to help...

PLEASE HELPPPP!!!!!
Miguel thinks the science teachers in his school give more homework than the math teachers. He is researching the number of hours middle school students in his school spend doing math and science homework each night.
The _____ includes all of the students in Miguel’s middle school.
A ___ possible is some students from each of the grades in the middle school.

Answers

Answer:

total

percentage

Step-by-step explanation:

total would be all percentage would be part

4. In one semester, Doug and Laura spent a combined 230 hours in the tutoring lab. If Doug
spent 10 hours less than twice the hours Laura did, how many hours did Doug spend in
the lab?

Answers

Answer:

80 hours

Step-by-step explanation:

let d represent doug, let l represent laura

first, set up a system of equations representing the problem:

since doug spent 10 less than twice the hours laura did, and we know that the total amount of hours they spent together is 230:

l=2d+10

d+l=230

then solve:

*first i rearranged the equations so i can solve this system of equations using elimination method*

l-2d=10

l+d=230

*subtract*

3d=240

d=80

so, doug spent 80 hours in the lab

.What is the value of the expression: -4+65

Answers

Answer:

+61

Step-by-step explanation:

Answer:

61

Step-by-step explanation:

Please mark as brainliest!

What is Fourteen less than seven times a number is 15

Answers

Answer:

29/7     or     4  1/7

Step-by-step explanation:

Let x be the unknown number.

7 times a number is 7x,

and then 14 less than that would be 15.

7x-14=15

Now simplify by adding 14 and dividing by 7

7x=29

x=29/7    or 4 1/7

Please help me with this I need to know

Answers

Answer:Just multiply Step-by-step explanation:do 12x10x20=2,400

PLEASE HELP ILL GIVE BRAINLIEST AND 20 POINTS!!!!!

The 8th grade is holding a fundraiser to raise money for an end of the y ear party. They are selling T-shirts and Caps to raise money. They make $15 profit from each T-shirt and $5 profit from each hat. Their goal is to raise $900.

Part A: Write and equation that represent this situation.

Part B: Find 3 combinations of shirts and caps that will achieve their goal of raising $900.

A CORRECT ANSWER WILL HAVE 4 PARTS!​

Answers

For each t-shirt sold, which I'll call t, 8th grade makes $15.

For each hat sold, which I'll call h, 8th grades makes $5.

They want to raise $900

A: The equation to represent this situation is 15t+5h=900 because if 8th grade adds up all the profits from both hats and t-shirts, the goal is to make $900, so the total profit from shirts and hats should equal 900 dollars.

B: I'm just going to choose random numbers. Let's say nobody wanted to buy a hat from the 8th graders (h=0). You'd end up with

15t+5(0)=900

15t=900

t=60 - If they sold 0 hats they would have sold 60 shirts to raise $900

Now let's say it was the other way around - nobody wanted to buy t-shirts

15(0)=5h=900

5h=900

h=180 - If they sold 0 t-shirts they'd have to sell 180 hats to raise $900

Finally let's say they sold 30 t-shirts

15(30)+5h=900

450+5h=900

5h=450

h=90 - They'd have to sell 30 t-shirts and 90 hats to raise $900

What are the coordinates of B’ if Triangle ABC is reflected over the x-axis?

Answers

Answer:

the coordinates of b if it is reflected over the x-axis (-2,5)

If a price increases by 16%, what number can we multiply the old price by to get the new price?

Answers

Answer:

Multiply by 1.16

Step-by-step explanation:

Answer:

Multiply it by 0.16

How many sides are on a hexahectaenneacontakaiheptagon?

A. 697

B. 640

C. 546

E. a hexahectaenneacontakaiheptagon is not a real polygon

Answers

Answer:

E

Step-by-step explanation:

I have never heard of it in my entire life.

Answer and Step-by-step explanation:

A is the correct answer.

The shape called hexahectaenneacontakaiheptagon has 697 sides.

#teamtrees #PAW (Plant And Water)

Simplify the fraction 84/96.

Answers

Answer:

7/8

Step-by-step explanation:

U have to use the highest common factor and the lowest common denominator

Answer:

[tex] \frac{7}{8} = 0.875 [/tex]

Step-by-step explanation:

devide the numerator and denumerator by nine

100Pts fast plz
A triangular pen is modeled by △ABC. The vertices of △ABC are A(0, 8), B(12, 3), and C(7, –9). What is the area of the pen?

Answers

Answer:

The area of the triangle is 84.511 square units.

Step-by-step explanation:

First step, we need to calculate lengths of line segments AB, BC and AC by Pythagorean Theorem:

AB:

[tex]AB = \sqrt{(12-0)^{2}+(3-8)^{2}}[/tex]

[tex]AB = 13[/tex]

BC:

[tex]BC = \sqrt{(7-12)^{2}+(-9-3)^{2}}[/tex]

[tex]BC = 13[/tex]

AC:

[tex]AC = \sqrt{(7-0)^{2}+(-9-8)^{2}}[/tex]

[tex]AC \approx 18.385[/tex]

Now, we can determine the area of the triangle ([tex]A[/tex]) by Heron's formula:

[tex]A = \sqrt{s\cdot (s-AB)\cdot (s-BC)\cdot (s-AC)}[/tex] (1)

[tex]s = \frac{AB+BC+AC}{2}[/tex] (2)

Where [tex]s[/tex] is the semiperimeter of the triangle.

If we know that [tex]AB = 13[/tex], [tex]BC = 13[/tex] and [tex]AC \approx 18.385[/tex], then the area of the triangle is:

[tex]s = 22.193[/tex]

[tex]A = 84.511[/tex]

The area of the triangle is 84.511 square units.

RADICALS
Put the numbers in order from smallest to largest:



NEED HELP ASAP PLEASE!!!!

Answers

Answer:

,square root of 15;3;4;square root of 21 ;square root of 24 ;5;6;square root of 40

Step-by-step explanation:

the square roots ain't perfect square so make them decimals to know which one is bigger

Helpppp!!
What is the value of x and y?

Answers

Answer:

x=8 and y =40

Step-by-step explanation:

this is the answer

Kevin has a stamp collection he keeps 10 of the stamps in an album which is only 5% of his entire

Answers

Answer:

200 stamps should be Kevin whole collection.

Step-by-step explanation:

What's the question exactly? I don't know, I just wrote something I think you might find useful.

Answer:

20 stamps..

You didn't give the whole question but I am GUESSING that it is what is his total amount of stamps in his entire album..

--

10 x 2 = 20

Last season, two running backs on the Steelers
football team rushed for a combined total of
1550 yards. One running back ran for 450 yards
more than the other. How many yards did they
each run?

Answers

Answer:

Step-by-step explanation:

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. this is the equation that was used

         x + y = 1550

         y  = 4x

Pleaseeee helpppp it’s due in 6 minutes helpp!! Explain

Answers

Answer:

I might be wrong but since ur in a rush: 173

Step-by-step explanation:

Answer:

287.25 miles in 5.75 hours

Step-by-step explanation:

so he was first driving at 48mph because 168/3.5=48

5 miles per hour faster than that is 53mph

53*2.25=119.25

then we add 119.25 and 168

7.) Which expression makes the following equation true? 25x + 15y + (-18x - 1 point
6y) =_______+9y *
A.-43x
B.-7x
C.7x
D.43x

Answers

Answer:

sorry i need this for a challenge :)

Step-by-step explanation:

the answer is letter A

HELP ME NOW
04 Fill in the blank Drag and Drop
Raven has driven 90 miles, which represents 30% of the total distance she diving
What is the total distance Raven is driving, and how many miles does she have left to drive
Drag a number into each box to complete the sentences
Raven is driving a total distance of
miles. She has
miles left to die
11 27
11 30
11 63
1 90
11 117
11 210
11 300
11990

Answers

Answer:

its blurry

Step-by-step explanation:

Element X is a radioactive isotope such that its mass decreases by 67% every year. If
an experiment starts out with 740 grams of Element X, write a function to represent
the mass of the sample after t years, where the daily rate of change can be found
from a constant in the function. Round all coefficients in the function to four decimal
places. Also, determine the percentage rate of change per day, to the nearest
hundredth of a percent.

Answers

Answer:

Step-by-step explanation:

X is mass which I s decrease. If you have 740 grams of element x and you add the function.per the rate day you will have a hundredth percent.

Answer:

f(t)=740(0.9970)^365t

0.30% decrease per day

HELP ME WALLAHI THIS IS HARD WALLAHI HELP ME

Answers

Answer: It’s C

Step-by-step explanation:

Mr Kinney biology class completed a lab to determine blood type. The results are reported in the frequency table. What is the relative frequency of a student having o type blood? 0.1 0.2 0.3 0.4

Answers

Answer:

o . ooo 2 and dr 45009.7 ok byy

answer now please 10 points come earn them

Answers

Answer:

B

Step-by-step explanation:

Arkadaşım cevap istiyorsan benim soruma cvp ver

Answer:

38

Step-by-step explanation:

sub everything

4(5)-3(2)(-3)=38

Which expression is NOT equivalent to -6 x (1/3 + 1/3)
A. -6/3 + 1/3
B. -6 x 2/3
C. -6 x (2x 1/3)
D.(1/3 + 1/3) x (-6)

Answers

A -6/3 + 1/3 I believe is the answer

HelllpFind an equation of a line that contains the points (-3,-1) and (2,-2). Write the equation in slope-intercept form.

Answers

Answer:

y = -1/5x -8/5

Step-by-step explanation:

(-3,-1) and (2,-2)

m=(y2-y1)/(x2-x1)

m = ( -2 + 1)/(2 + 3)

m = (-1)/(5)

m = -1/5

y - y1 = m(x - x1)

y + 1 = -1/5(x + 3)

y + 1 = -1/5x -3/5

y = -1/5x -8/5

Find the surface area of the right triangular prism (above) using its net (below).
units

Answers

Answer:

120 units^2

Step-by-step explanation:

(12)(5)(0.5)(2) + (12)(2) + (13)(2) + (5)(2) = 120 units^2

I need help to do this dont know how to do!

Answers

Answer:

Step-by-step explanation:

Even I need help with that

I DONT WANT HOW TO DO IT JUST THE ANSWER

Answers

Answer:

87.5

Edited: Yea should be 56, misread it LOL.

Appoligise to that silly mistake

Step-by-step explanation:

56 trust me homie yuh
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