2.1 Matrix Operations

Question 1

Complete the sentence:

Each column of AB is a……………..

Answer 1

linear combination of the columns of A using weights from the corresponding column of B

Question 2

Complete the sentence:

If A is an m x n matrix, and if B is ……..

Answer 2

an n x p matrix with columns b1……bp then the product AB is the m xp matrix whose columbs are Ab1….Abp

Question 3

AB ____ BA

Answer 3

does not equal

Question 4

The cancellation laws _________ for ________

Answer 4

do not hold

matrix multiplicaiton

Question 5

If a product AB is the zero matrix………

Answer 5

you cannot conclude in general that ether A=0 or B=0

Question 6

(A^T)^T = ?

Answer 6

A

Question 7

(A + B)^T = ?

Answer 7

A^T + B^T

Question 8

for any scalar r, (rA)^T =?

Answer 8

r(A^T)

Question 9

(AB)^T = ?

Answer 9

B^T A^T

Question 10

The transpose of a product of matrices……….

Answer 10

equals the product of their transposes in reverse order

Question 11

associative law of multiplication

Answer 11

A(BC) = (AB)C

Question 12

left distributive law

Answer 12

A(B+C) = AB + AC

Question 13

right distributive law

Answer 13

(B+C)A = BA + CA

Question 14

scalar r

Answer 14

r(AB) = (rA)B = A(rB)

Question 15

identity for matrix multiplication

Answer 15

I(sub m)A= A = AI(sub n)