Q37 of 98 Page 310

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


More from this chapter

All 98 →
35

Solve each of the following systems of equations using matrix method.

x - y = 3;


2x + 3y + 4z = 17;


y + 2z = 7.


 36

Solve each of the following systems of equations using matrix method.

4x + 3y + 2z = 60;


x + 2y + 3z = 45;


6x + 2y + 3z = 70.


 38

If A = , find A - 1.

Using A - 1, solve the following


system of linear equations:


2x + y + z = 1;


X – 2y – z = ;


3y – 5z = 9.


HINT: Here A = ,


X = and B = .


 39

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.