Matrix Problem-Solving 1: Matrix Addition, Subtraction, and Multiplication

 Matrix Problem-Solving 1: Matrix Addition, Subtraction, and Multiplication

Problem Set

1. Add the matrices:

   $$A = \begin{pmatrix} 2 & 4 \\ 6 & 8 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & 3 \\ 5 & 7 \end{pmatrix}$$
   

2. Subtract the matrices:

   $$A = \begin{pmatrix} 9 & 7 \\ 5 & 3 \end{pmatrix}, \quad B = \begin{pmatrix} 3 & 5 \\ 7 & 9 \end{pmatrix}$$
   

3. Multiply the matrices:

   $$A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}$$
   

4. Add the following 3x3 matrices:

   $$C = \begin{pmatrix} 5 & 2 & 3 \\ 4 & 6 & 1 \\ 7 & 8 & 9 \end{pmatrix}, \quad D = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}$$

5. Subtract the matrices:

   $$E = \begin{pmatrix} 10 & 12 \\ 14 & 16 \end{pmatrix}, \quad F = \begin{pmatrix} 6 & 5 \\ 4 & 3 \end{pmatrix}$$

6. Multiply the matrices:

   $$G = \begin{pmatrix} 3 & 4 \\ 2 & 1 \end{pmatrix}, \quad H = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix}$$
   

7. Add the matrices:

   $$I = \begin{pmatrix} 4 & 5 & 6 \\ 1 & 2 & 3 \\ 7 & 8 & 9 \end{pmatrix}, \quad J = \begin{pmatrix} 3 & 2 & 1 \\ 6 & 5 & 4 \\ 9 & 8 & 7 \end{pmatrix}$$

8. Subtract the matrices:

   $$K = \begin{pmatrix} 11 & 14 & 17 \\ 8 & 10 & 12 \\ 5 & 6 & 7 \end{pmatrix}, \quad L = \begin{pmatrix} 5 & 6 & 7 \\ 3 & 4 & 5 \\ 1 & 2 & 3 \end{pmatrix}$$

9. Multiply the matrices:

   $$M = \begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{pmatrix}, \quad N = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$$
   

10. Add the following 2x3 matrices:

$$O = \begin{pmatrix} 3 & 5 & 7 \\ 2 & 4 & 6 \end{pmatrix}, \quad P = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix}$$

11. Subtract the matrices:

$$Q = \begin{pmatrix} 8 & 9 & 10 \\ 11 & 12 & 13 \end{pmatrix}, \quad R = \begin{pmatrix} 3 & 3 & 3 \\ 4 & 4 & 4 \end{pmatrix}$$

12. Multiply the matrices:

$$S = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}, \quad T = \begin{pmatrix} 4 & 5 \\ 6 & 7 \end{pmatrix}$$

13. Add the following 4x1 matrices:

$$U = \begin{pmatrix} 1 \\ 2 \\ 3 \\ 4 \end{pmatrix}, \quad V = \begin{pmatrix} 5 \\ 6 \\ 7 \\ 8 \end{pmatrix}$$

14. Subtract the matrices:

$$W = \begin{pmatrix} 9 \\ 10 \\ 11 \\ 12 \end{pmatrix}, \quad X = \begin{pmatrix} 3 \\ 4 \\ 5 \\ 6 \end{pmatrix}$$

15. Multiply the following 1x4 and 4x1 matrices:

$$Y = \begin{pmatrix} 2 & 4 & 6 & 8 \end{pmatrix}, \quad Z = \begin{pmatrix} 1 \\ 2 \\ 3 \\ 4 \end{pmatrix}$$

16. Add the matrices:

$$AA = \begin{pmatrix} 4 & 6 \\ 7 & 9 \end{pmatrix}, \quad BB = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$$

17. Subtract the matrices:

$$CC = \begin{pmatrix} 8 & 5 \\ 7 & 4 \end{pmatrix}, \quad DD = \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}$$

18. Multiply the matrices:

$$EE = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix}, \quad FF = \begin{pmatrix} 9 & 10 \\ 11 & 12 \end{pmatrix}$$

19. Add the matrices:

$$GG = \begin{pmatrix} 12 & 14 & 16 \\ 18 & 20 & 22 \end{pmatrix}, \quad HH = \begin{pmatrix} 1 & 1 & 1 \\ 2 & 2 & 2 \end{pmatrix}$$

20. Subtract the matrices:

$$II = \begin{pmatrix} 10 & 9 & 8 \\ 7 & 6 & 5 \end{pmatrix}, \quad JJ = \begin{pmatrix} 4 & 3 & 2 \\ 1 & 0 & -1 \end{pmatrix}$$

21. Multiply the following 2x3 and 3x2 matrices:

$$KK = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix}, \quad LL = \begin{pmatrix} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{pmatrix}$$

22. Add the matrices:

$$MM = \begin{pmatrix} 6 & 6 \\ 7 & 7 \\ 8 & 8 \end{pmatrix}, \quad NN = \begin{pmatrix} 1 & 1 \\ 2 & 2 \\ 3 & 3 \end{pmatrix}$$

23. Subtract the matrices:

$$OO = \begin{pmatrix} 14 & 15 & 16 \\ 17 & 18 & 19 \\ 20 & 21 & 22 \end{pmatrix}, \quad PP = \begin{pmatrix} 4 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix}$$

24. Multiply the matrices:

$$QQ = \begin{pmatrix} 3 & 2 \\ 1 & 4 \\ 5 & 6 \end{pmatrix}, \quad RR = \begin{pmatrix} 7 & 8 \\ 9 & 10 \end{pmatrix}$$

25. Add the matrices:

$$SS = \begin{pmatrix} 5 & 10 \\ 15 & 20 \end{pmatrix}, \quad TT = \begin{pmatrix} 2 & 4 \\ 6 & 8 \end{pmatrix}$$

Solutions

1. $A+B$

$$\left(\begin{array}{cc}3& 7\\ 11& 15\end{array}\right)$$

2. $A - B$
   

$$\begin{pmatrix} 6 & 2 \\ -2 & -6 \end{pmatrix}$$

3. $A\times B$

$$\begin{pmatrix} 4 & 6 \\ 10 & 12 \end{pmatrix}$$

4. $C + D$
   

$$\begin{pmatrix} 6 & 4 & 6 \\ 8 & 11 & 7 \\ 14 & 16 & 18 \end{pmatrix}$$

5. $E - F$
   

$$\begin{pmatrix} 4 & 7 \\ 10 & 13 \end{pmatrix}$$

6. $G \times H$
   

$$\begin{pmatrix} 43 & 50 \\ 19 & 22 \end{pmatrix}$$

7. $I+J$

$$\begin{pmatrix} 7 & 7 & 7 \\ 7 & 7 & 7 \\ 16 & 16 & 16 \end{pmatrix}$$

8. $K-L$

$$\begin{pmatrix} 6 & 8 & 10 \\ 5 & 6 & 7 \\ 4 & 4 & 4 \end{pmatrix}$$

9. $M \times N$
   

$$\begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{pmatrix}$$

10. $O+P$

$$\begin{pmatrix} 4 & 6 & 8 \\ 3 & 5 & 7 \end{pmatrix}$$

11. $Q - R$
    

$$\begin{pmatrix} 5 & 6 & 7 \\ 7 & 8 & 9 \end{pmatrix}$$

12. $S \times T$
    

$$\begin{pmatrix} 8 & 10 \\ 18 & 21 \end{pmatrix}$$

13. $U+V$

$$\begin{pmatrix} 6 \\ 8 \\ 10 \\ 12 \end{pmatrix}$$

14. $W - X$
    

$$\begin{pmatrix} 6 \\ 6 \\ 6 \\ 6 \end{pmatrix}$$

15. $Y \times Z$
    

$$\begin{pmatrix} 60 \end{pmatrix}$$

16. $AA+BB$

$$\begin{pmatrix} 5 & 8 \\ 10 & 13 \end{pmatrix}$$

17. $CC - DD$
    

$$\begin{pmatrix} 6 & 4 \\ 4 & 2 \end{pmatrix}$$

18. $EE\times FF$

$$\begin{pmatrix} 129 & 140 \\ 173 & 188 \end{pmatrix}$$

19. $GG + HH$
    

$$\begin{pmatrix} 13 & 15 & 17 \\ 20 & 22 & 24 \end{pmatrix}$$

20. $II - JJ$
    

$$\begin{pmatrix} 6 & 6 & 6 \\ 6 & 6 & 6 \end{pmatrix}$$

21. $KK \times LL$
    

$$\begin{pmatrix} 58 & 64 \\ 139 & 154 \end{pmatrix}$$

22. $MM + NN$
    

$$\begin{pmatrix} 7 & 7 \\ 9 & 9 \\ 11 & 11 \end{pmatrix}$$

23. $OO - PP$

$$\begin{pmatrix} 10 & 10 & 10 \\ 10 & 10 & 10 \\ 10 & 10 & 10 \end{pmatrix}$$

24. $QQ \times RR$
    

$$\begin{pmatrix} 31 & 36 \\ 43 & 48 \\ 67 & 78 \end{pmatrix}$$

25. $SS+TT$

$$\begin{pmatrix} 7 & 14 \\ 21 & 28 \end{pmatrix}$$