Q. 39 Using

# If A = andB = , find AB.Hence, solve the system of equations:x – 2y = 10,2x + y + 3z = 8 and- 2y + z = 7.HINT: AB = (11)I = A = IA - 1 = B.

Given,

A = , B =

AB =

AB =

AB =

AB =

AB = 11

AB = 11I

Pre - multiplying by A - 1

A - 1AB = 11 A - 1I

IB = 11 A - 1

B = 11 A - 1

A - 1 = B

Given set of lines are : -

x – 2y = 10

x + y + 3z = 8

- 2y + z = 7

Converting following equations in matrix form,

AX = C

Where A = ,X = , C =

Pre - multiplying by A - 1

A - 1AX = A - 1C

IX = A - 1C

X = A - 1C

X = BC

=

=

=

x = 4 , y = - 3 , z = 1

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