Tutorial4.pdf

UNIVERSITI PUTRA MALAYSIA
FAKULTI SAINS
MTH 3004 PENGENALAN KEPADA MATEMATIK EKONOMI DAN PERNIAGAAN
Tutorial 4
0 0 −11 0 
1 −1 0
1. If A=  and B = 2 −1 0  and C = 2 −1. Perform the indicated
0 1 1
0 0 2 0 1 
operations:
(a) AB (b) AB − 2CB
T
(b) (BA) (d)
˓- ˕˔

1 2 
 1 3 1 0 1 2 −1
A B  C  D 
2. If = 0 −1, = , =  and = .
4 −11 21 0 2 
2 0 
Compute the indicated matrices if possible:
(a) 3AT + D (b) (B − C)T
(c) 2BT − 3C T (d) 2(B)B T
T
(e) (3 CB) (f) (D − 2AT )

3. Write the following system of equations into the matrix form, and solve by finding the
inverse matrix.
(a) Ÿ˲. Ŷ˳
.ŸŴ (b) ˲- ˳
ź
ŷ˲- Ÿ˳
ŶŹ ŷ˲. Ŷ˳
ŷ

(c) ź˲- ŷ˳
ź (d) Ź˲. Ŷ˳
ŵ
Ŷ˲- Ÿ˳
ŵŸ ŷ˲- ˳
Ŷ

(e) Ŷ˲. ŷ˳
.ŵ (f) ˲. Ŷ˳
.
.ŵŴ˲- ŵŹ˳
Ź .Ÿ˲- ˳
ŵŴ

4. Convert the following system of equations into the matrix form, and write the respective
augmented matrix. Solve the matrix using Gaussian Elimination method.
(a) Ÿ˲. Ŷ˳
.ŸŴ (b) ˲- ˳
ź
ŷ˲- Ÿ˳
ŶŹ ŷ˲. Ŷ˳
ŷ

(c) ź˲- ŷ˳
ź (d) Ź˲. Ŷ˳
ŵ
Ŷ˲- Ÿ˳
ŵŸ ŷ˲- ˳
Ŷ

.******@UPM
(e) Ŷ˲. ŷ˳
.ŵ (f) ˲. Ŷ˳
.
.ŵŴ˲- ŵŹ˳
Ź .Ÿ˲- ˳
ŵŴ

(g) Ŷ˲# . ˲$ - ˲%
.Ŷ (h) ˲# - ˲$ - ˲%
ŵ
˲# - Ÿ˲$ . ˲%
Ź ŷ˲# . Ŷ˲$ - ˲%
.ŵ
˲# - ˲$ - ˲%
ź ˲# - ŷ˲$ . ˲%
ŵŵ

(i) ŷ˲# . ˲$ - Ŷ˲%
ź (j) .˲# - Ŷ$