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 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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