Question

Matrix A is a 1 x 3
Matrix B is a 3 x 1 Matrix

Which one of the follow matrix expressions involving A and B is defined?

2B x 3A

or

A^2 B

...........................
It seems to me both are feasible
But apparently A^2B is wrong according to the textbook

Answer 1

mxn matrix can multiply an nxr matrix

Answer 2

No idea what that means.

Answer 3

its A^2 B

Answer 4

oooops did it wrong sry

Answer 5

nevermind that

Answer 6

for example
3x2 * 2x7 matrix is defined, because the 2's match

Answer 7

a mxn matrix has m rows, n columns
a n x r matrix has n rows and r columns

Answer 8

yeah so if a= 4x4

a^2= 1x3 * 1x3

So (A) 1x3 x (B) 3x1 also match

So cant both be expressed?

Answer 9

disregard the 4x4 sorry

Answer 10

so both can be expressed but apparently the answer is only 2B x 3A

Answer 11

lets make a notation
[3x1] means a matrix that has dimensions 3 rows and 1 column

Answer 12

I will use * to indicate matrix multiplication
2B * 3A : 2[3x1] * 3[1x3] = [3x1 ] * [1x3]
multiplying a matrix by a scalar does not change dimensions
this is defined

Answer 13

A^2 * B : [1x3 ] * [1x3] * [ 3 x 1]

here we see it is not defined because of the 3 and 1
A*A is not defined

Answer 14

A^2 B = A*A*B
but A*A is not defined , so the entire product cannot be defined

Answer 15

So the product of 2B * 3A = 3x3

But A^2 = 1x1

So cant both be defined?

Answer 16

no , A^2 is not 1x1, its not defined at all

Answer 17

dimension mismatch error

Answer 18

I meant A^2 x B = 1x1

Answer 19

Sorry

Answer 20

you cant multiply A by A

Answer 21

nope, A^2 * B is not defined. you cant multiply an undefined matrix by something else

Answer 22

A^2 being undefined

Answer 23

yeah thanks understand now

Answer 24

you should do the multiplication from left to right
A^2B = AAB