Q. 215.0( 1 Vote )

# Solve for using properties of determinants.ORUsing elementary row operations find the inverse of a matrix and hence solve the following system of equations

We have,

Applying C1 C1 + C2 + C3, we get

Taking common (3a – x) from the first column, we get

Applying R2 R2 – R1, we get

Applying R3 R3 – R1, we get

Expanding along the first column, we get

=(1)[(2x)(2x) – (-2x)(-2x)]

= 4x2 – 4x2

= 0

= Rhs

Hence Proved

OR

We have,

We have to find A-1 and

Firstly, we find |A|

Expanding |A| along C1, we get

= 3[-3 – (-4)] – 2[-3 – (-4)]

= 3(1) – 2(1)

= 1

Now, we have to find adj A and for that we have to find co-factors:

Now, the system of linear equation is

3x – 3y + 4z = 21

2x – 3y + 4z = 20

-y + z = 5

We know that, AX = B

Here,

and we can see that this matrix is similar to the given matrix.

X = A-1B

x = 1, y = -2 and z = 3

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