Q. 215.0( 1 Vote )

# Solve for using properties of determinants.

**OR**

Using elementary row operations find the inverse of a matrix and hence solve the following system of equations

Answer :

We have,

Applying C_{1}→ C_{1} + C_{2} + C_{3}, we get

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

Applying R_{2}→ R_{2} – R_{1}, we get

Applying R_{3}→ R_{3} – R_{1}, we get

Expanding along the first column, we get

=(1)[(2x)(2x) – (-2x)(-2x)]

= 4x^{2} – 4x^{2}

= 0

= Rhs

Hence Proved

**OR**

We have,

We have to find A^{-1} and

Firstly, we find |A|

Expanding |A| along C_{1}, 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^{-1}B

∴ x = 1, y = -2 and z = 3

Rate this question :

Using matrices, solve the following system of equations:

2x + 3y + 3z = 5, x – 2y + z = – 4, 3x – y – 2z = 3

Mathematics - Board PapersIf find Using solve the system of equation

Mathematics - Board PapersSolve for using properties of determinants.

**OR**

Using elementary row operations find the inverse of a matrix and hence solve the following system of equations

Mathematics - Board Papers