Q. 295.0( 1 Vote )

# Using matrices, solve the following system of linear equations:x - y + 2z = 73x + 4y - 5z = - 52x - y + 3z = 12ORUsing elementary operations, find the inverse of the following matrix:

Given; x - y + 2z = 7

3x + 4y - 5z = - 5

2x - y + 3z = 12

AX = B

X = A - 1B

|A| = 1(12 − 5) + 1(9 + 10) + 2(−3 − 8)

= 7 + 19 − 22

= 4 ≠ 0

A - 1 exists

Cofactors of A are;

A11 = 7 A12 = −19 A13 = −11

A21 = 1 A22 = −1 A23 = −1

A31 = −3 A32 = 11 A33 = 7

x = 2, y = 1, z = 3 is the Required solution.

OR

Given;

A = IA

R1 2R1 + R3

R2 R2 − R1

R2 R2 − R1

R1 R1 + 3R2 and R3 R3 − 3R1

R2 −R2

R3 R3 + 8R2

R1 R1 + 1/2 R3

R2 R2 − R3 and R3 1/2 R3

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