1. Using matrix method, solve the following system of equations :

2/x + 3/y + 10/z = 4, 4/x - 6/y + 5/z = 1, 6/x + 9/y - 20/z = 2

2. For what value of x, the matrix [5-x x+1

2 4 ] is singular?

1.

Let 

Then the given system of equations is as follows:

This system can be written in the form of AX = B, where

A

Thus, A is non-singular. Therefore, its inverse exists.

Now,

A11 = 75, A12 = 110, A13 = 72

A21 = 150, A22 = −100, A23 = 0

A31 = 75, A32 = 30, A33 = − 24

2.

We know that a square matrix is singular if |A| = 0

 

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1. See there is nothing to panic just becoz your matrix X now consists of 1/x,1/y&1/z. Just substitute 1/x=p, 1/y=q & 1/z=r and proceed as usual!!  After u have found the value of p,r&r put the p=1/x, q=1/y & r=1/z.....

2. For a matrix to be singular its determinant must be equal to zero. So, we have: 2(5-x)-4(x+1)=0 =>x=1

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