explain solution rd sharma class 12 chapter determinants exercise 5.5 question 4 maths
Hint: The system has non-trivial solution implies that the determinant is zero.
Firstly, form 3x3 matrix from the given equations:
Let A = [, 2, 3 ]
[ 2 0 ]
We know that,
Expanding through first row,
As it satisfies the given equation,
So, the given linear equation transforms into:
Now, the above equations can be represented in matrix form i.e.
Now, Put z = k from first two equations, we get:
Now, By Crammer’s rule:
It also satisfies the third equation.
Hence, , and where