Matrices Mulitiplication Sample

SCI102 Tutorial Week 3 Answers

Equations in Matrix form 1. -13-22xy= 910
A= -13-22, X=xy and B=910
AX = B
X = A-1B |A| = - 2 – (-6) = 4
A-1 = 14 2-32-1 and X= 14 2-32-1910=14 18-3018-10

x = -12/4 and y = 8/4

x = - 3 and y = 2

2. A= 24-12, X=xy and B=06
AX = B
X = A-1B |A| = 4 – (- 4) = 8
A-1 = 18 2-412 and X= 18 2-41206=18 0-240+12

x = -24/8 and y = 12/8

x = - 3 and y = 3/2

3. A= 3243, X=xy and B=45

AX = B
X = A-1B |A| = 9 – 8 = 1
A-1 = 11 3-2-43 and X= 3-2-4345= 12-10-16+15

x = 2 and y = - 1

4. (a) A= 5327 |A| = 35 – 6 = 29

A-1 = 1AadjA A-1=1297-3-25

(b) A= 45023-1204
A-1= 1AadjA
First find the minor of A minor A= 1210-62016-10-5-42 cf A= minorAX place matrix=1210-62016-10-5-42+-+-+-+-+

cf A= 12-10-6-201610-542

|A| = 4 X 12 + 5 X -10 + 0 X – 6 = 48 – 50 = - 2

Transpose of cf A= 12-20-5-10164-6102

A-1=-1212-20-5-10164-6102=-6102.55-8-23-5-1

5. 3x + 6y + 5z = 7 x + y + z = 3
2x + 6y + 4z = 4 A= 365111264 X= xyz B= 734
AX = B
X = A-1B
A-1= 1AadjA
First find the minor of A minor A= -224-6261-2-3 cf A= minorAX place matrix=-224-6261-2-3+-+-+-+-+

cf A= -2-2462-612-3

|A| = 3 X - 2 + 6 X - 2 + 5 X 4 = - 6 – 12 + 20 = 2

Transpose of cf A= -261-2224-6-3
X=12-261-2224-6-3734=12-14+18+4-14+6+828-18-12
x=82, y=02 and z= -22 x = 4, y = 0 and z = -