152 CHAPTER 8. MATRICES

a computation in matlab, you ought to go to >> and type “clear all” and then enter. Thatway, you can use the symbols again with different definition. If you don’t do the “clear all”thing, it will go on thinking that A is what you defined earlier.

8.8 Exercises1. Here are some matrices:

A =

(1 2 32 1 7

),B =

(3 −1 2−3 2 1

),

C =

(1 23 1

),D =

(−1 22 −3

),E =

(23

).

Find if possible −3A,3B−A,AC,CB,AE,EA. If it is not possible explain why.

2. Here are some matrices:

A =

 1 23 21 −1

 ,B =

(2 −5 2−3 2 1

),

C =

(1 25 0

),D =

(−1 14 −3

),E =

(13

).

Find if possible −3A,3B−A,AC,CA,AE,EA,BE,DE. If it is not possible explainwhy.

3. Here are some matrices:

A =

 1 23 21 −1

 ,B =

(2 −5 2−3 2 1

),

C =

(1 25 0

),D =

(−1 14 −3

),E =

(13

).

Find if possible −3AT ,3B− AT ,AC,CA,AE,ET B,BE,DE,EET ,ET E. If it is notpossible explain why.

4. Here are some matrices:

A =

 1 23 21 −1

 ,B =

(2 −5 2−3 2 1

),

C =

(1 25 0

),D =

(−14

),E =

(13

).

Find the following if possible and explain why it is not possible if this is the case.

AD,DA,DT B,DT BE,ET D,DET .