If A = and

B = , find AB.

Hence, solve the system of equations:

x – 2y = 10,

2x + y + 3z = 8 and

- 2y + z = 7.

HINT: AB = (11)I = A = I

A ^{- 1} = B.

Given,

A = , B =

AB =

AB =

AB =

AB =

AB = 11

AB = 11I

Pre - multiplying by A ^{- 1}

A ^{- 1}AB = 11 A ^{- 1}I

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 ^{- 1}AX = A ^{- 1}C

IX = A ^{- 1}C

X = A ^{- 1}C

X = BC

=

=

=

∴ x = 4 , y = - 3 , z = 1