# If A = , find A - 1.Using A - 1, solve the following system of equations:2x – 3y + 5z = 11;3x + 2y – 4z = - 5;x + y – 2z = - 3.

Given,

A = A - 1 = The determinant of matrix A is

|A| = = 2( 2 × - 2 – ( - 4)×1) + 3(3× - 2 – ( - 4)×1) + 5(3×1 – 2×1)

= 2( - 4 + 4 ) + 3( - 6 + 4 ) + 5( 3 – 2 )

= 2(0) + 3( - 2) + 5(1)

= - 6 + 5

= - 1

|A| ≠ 0

A - 1 is possible.

AT = Adj(A) = A - 1 = A - 1 = A - 1 = Given set of lines are : -

2x – 3y + 5z = 11

3x + 2y – 4z = - 5

x + y – 2z = - 3

Converting following equations in matrix form,

AX = B

Where A = , X = , B = Pre - multiplying by A - 1

A - 1AX = A - 1B

IX = A - 1B

X = A - 1B  =  =  = x = 1 , y = 2 , z = 3

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