The document provides examples of matrix operations including multiplication and addition. It gives the matrices A, B, C, D, E, F, G, H and defines various expressions involving combinations of these matrices. It then shows the step-by-step workings to calculate selected expressions, including finding the products AB and BA, adding and subtracting matrices, and combining scalar values with matrices. It concludes that the factoring formula (C+D)(C-D) does not work for matrices C and D.

1. Example D: Let A = and B = ,
Matrix Operations
0 23 –1 –2
2 4 0 –1 4
find AB and BA if it's possible.
AB = 3 –1 –2
2 4 0
0 2
–1 4 is undefined due to their sizes.
To multiply BA =
0 2
–1 4
3 –1 –2
2 4 0
start with the 1st row of B, multiply it in order against
each column of A to get the 1st row of the product.
Then use the 2nd row of B and repeat the process to
get the 2nd row of the product, then the process stops.
BA =
0 2
–1 4
3 –1 –2
2 4 0
=
0+4 0+8 0+0
–3+8 1+16 2+0
=
5 17 2
4 8 0

2. Matrix Operations
A =
Ex. A. Given the following matrices, combine the following
matrix expressions if possible. If it’s not possible, state so.
1
2
0
–1
2 –1 B =
1
0
C =2
2
1
0
–1
D =
0 2F =E = 2
1
0
–1
0
–1
1 00
G = 0
1
1
0
0
1
–1 20
H = 2
1
0
–2
11
1. 2A 2. –3B 3. 2C – 3D 4. A + B 5. 3A + 2F
6. AB vs. BA 7. CA vs. AC
16. FH + B
9. BG vs. GB8. BF vs. FB
10. EF 11. CD + DC 12. EG – GE 13. GH – HG
14. FC – 2A 15. DA + 3F 17. HF – B
18. C2 – D2 19. (C + D)(C – D)
20. The answers for 18 and 19 are different so C2 – D2 ≠ (C + D)(C – D),
why doesn’t this factoring formula work for matrices?

3. Matrix Operations
Ex. B. Given the following matrices, calculate the following
matrix-algebraic expressions.
1
2
0
–1
u =
2
A =
02
1
0
–1
B =
F =E = 2
1
0
–1
0
–1
1 00
x =0
1
1
0
0
1
–1 20
y =2
1
1
1. Au 2. Bv 3. Au + Bv 6. 2Bu – 3Bv5. 3A + 2F
v =
–1
2
0
1
–1
4. 2Av – 3Bu
7. Au – Bv + Av – Bu 8. Ex + Fy 9. EFx 10. FEy 11. F2x + E2y

4. Matrix Operations
(Answers to the odd problems) Exercise A.
1. 2A = (4 -2) 3. 2𝐶– 3𝐷 =
−1 1
−4 0 5. 3A + 2F = (6 1)
7. CA it’s not possible 9. BG it’s not possible
11. 𝐶𝐷 + 𝐷𝐶 =
1 −3
5 −3
13. HG it’s not possible 15. DA it’s not possible
17. HF it’s not possible 19. 𝐶 + 𝐷 𝐶 – 𝐷 =
5 0
3 0
Exercise B.
1. 𝐴𝑢 =
4
2
3. 𝐴𝑢 + 𝐵𝑣 =
1
0
5. It’s not possible
7. 𝐴𝑢 – 𝐵𝑣 + 𝐴𝑣 – 𝐵𝑢 =
1
−1
9. 𝐸𝐹𝑥 =
0
4
2
11. 𝐹2 𝑥 + 𝐸2 𝑦 =
2
6
0