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.

Question

Philoid · Accepted Answer

Given,

A = , B =

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