# If A = , find A - 1.Using A - 1, solve the followingsystem of linear equations:2x + y + z = 1;X – 2y – z = ;3y – 5z = 9.HINT: Here A = ,X = and B = .

Given,

A =

A - 1 =

The determinant of matrix A is

|A| =

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

= 2(10 + 3) – ( - 5) + (3)

= 26 + 5 + 3

= 34

|A| ≠ 0

A - 1 is possible.

AT =

A - 1 =

A - 1 =

Given set of lines are : -

2x + y + z = 1

X – 2y – z =

3y – 5z = 9

Converting the 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 = , z = -

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