Q. 295.0( 1 Vote )

Using matrices, solve the following system of linear equations:

x - y + 2z = 7

3x + 4y - 5z = - 5

2x - y + 3z = 12

OR

Using elementary operations, find the inverse of the following matrix:


Answer :

Given; x - y + 2z = 7

3x + 4y - 5z = - 5


2x - y + 3z = 12



AX = B


X = A - 1B


|A| = 1(12 − 5) + 1(9 + 10) + 2(−3 − 8)


= 7 + 19 − 22


= 4 ≠ 0


A - 1 exists


Cofactors of A are;


A11 = 7 A12 = −19 A13 = −11


A21 = 1 A22 = −1 A23 = −1


A31 = −3 A32 = 11 A33 = 7









x = 2, y = 1, z = 3 is the Required solution.


OR


Given;


A = IA



R1 2R1 + R3



R2 R2 − R1



R2 R2 − R1



R1 R1 + 3R2 and R3 R3 − 3R1



R2 −R2



R3 R3 + 8R2



R1 R1 + 1/2 R3



R2 R2 − R3 and R3 1/2 R3





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