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

Someone help me I don't know how to use garage band please help if you know how t

Answer 16

calc iii solution check

Answer 17

find max and min of x^2 + y^2 subject to the constraint x^2 - 8x +y^2 - 10y = 0

Answer 18

calc iii lagrange multipliers problem

Answer 19

Emotional effects of steroid use seem to depend on the _______ of the steroid used.

Answer 20

catlover462634
ASAP!!! PLEASE! I need this done and quick. im not sure why but i can even think of anything to do this.

Answer 21

Luella has a pond in her yard. She wants to surround it with 330 feet of fencing. The fencing is sold by the yard. How many yards should she buy?

Answer 22

someone check my answers
http://prntscr.com/mls3hl

Answer 23

https://i.imgur.com/Wjmpc6D.png

Answer 24

Assessment items
Assessment started: undefined.
Item 1

Read the passage.

Dark Star

Giselle leaned against the mahogany bay horse, stroking the white diam

Answer 25

Okay I was gone for a minute BUT I'M BACK NOW

Answer 26

the scatter plot presents Ray's monthly electricity bills and amount of time ray

Answer 27

Which word shares a connotative meaning with the word cheap as it is used in this sentence?

Ashley thought her parents were being cheap when they bought ge

Answer 28

Which revision fixes the dangling modifier in the sentence?

Rowing through the rapids, the canoe began to fill with water.

Answer 29

dangling modifier

Answer 30

Misplaced Modifiers

Answer 31

For which literary work did Joseph Heller use his military experiences as a prima

Answer 32

Calc III Tutorial: Lagrange Multipliers

Answer 33

Can someone translate this for me?

Answer 34

Find the interest due on $1,090 at 8% for 5 years.

43.60
68.13
436.00
681.25