Question

Prove that whenever A and B are matrices for which AB is defined, then (B^T)(A^T) is also defined. Then show (AB)^T=(B^T)(A^T). (transpose)

Answer 1

So what does it mean AB is defined?

Answer 2

I'm guessing, if A is an m x n matrix and B is an n x p matrix

Answer 3

...then AB will be defined as the m x p matrix

Answer 4

Well my book says the transpose of a product of any number of matrices is the product of the tranposes in the reverse order.

Answer 5

my prof always starts of a proof asking "What do we know"

Answer 6

So we know that AB is defined

Answer 7

I guess i'm having trouble understanding this whole "ijth" entry thing, I didn't understand it much in lecture and my book doesn't expand

Answer 8

can you tell me what topic it is?

Answer 9

n-Dimensional Geometry: Matrix Multiplication

the book says that the matrix product AB is the mxp matrix whose ijth entry is the dot product of the ith row of A and the jth column of B (considered as vectors in R^n)

Answer 10

check out this webpage it explains matrix multiplication in easy to understand language
http://www.purplemath.com/modules/mtrxmult.htm

Answer 11

thank you!

Answer 12

you're welcome

Answer 13

did that help?

Answer 14

a little, i looked into my book a bit more and convinced myself that the ijth entry of AB is \[\sum_{k}^{n}\] \[a _{ik}b _{kj}\] , which equals the jith entry of \[B ^{T}A ^{T}\] which is \[\sum_{k}^{n} b _{kj}a _{ik}\]

Answer 15

Math help

Answer 16

Math help

Answer 17

Joe takes part in math competitions. A particular contest consists of 25 multiple-choice questions, and each question has 5 possible answers.

Answer 18

CLICKBAIT

Answer 19

Math help

Answer 20

Math help please

Answer 21

For the graph, which are possible functions u0192 and g?

https://dlap.gradpoint.com/Resz/~0.WizMacW1O0YyUA6.3mlS9pk2V_dxq3Z3V_nFYjSGI1H7UJXF1eNTFTnwZ-I/7234256,D94/Assets/questions/quiz/precalculus/pcalexpo/IMG73460.png

Answer 22

i need some help please

Answer 23

Select the correct answer.
Read this excerpt from "The Third Philippic," written by Demosthenes in 342 B.

Answer 24

Jackson is teaching a class the concept of the binary number system. Which term w

Answer 25

Affirmative action policies were originally designed to _____.

make sure a certa

Answer 26

What two Democratic leaders constantly challenged President Carter during his adm

Answer 27

Is the function u0192(x) = xu2078 an exponential function? If so, identify the base.

Answer 28

Perform the arithmetic operation. Write it in the simplest form. 5 yd. 1 ft. - 2 yd.

Answer 29

The narrator's description of Kunthi as "a thin, slight girl" connotes that

Answer 30

Math help

Answer 31

I just write whatever comes to mind, so..ye.

- Endless -

Answer 32

Which term describes the point where the perpendicular bisectors of the three sid

Answer 33

Write the Standard Form of the line with x-intercept of 3 and y-intercept of 4.

Answer 34

math help, screenshot in comments