Question
If then exists
- For all real
- For positive real only
- For negative real only
- None of these
Hint:
We are given a matrix. We have to find the condition on the variable x so that the inverse of the matrix exist.
The correct answer is: For all real
The given matrix is
The inverse of matrix exists if it's determinant is non zero.
We will find the determinant of the given matrix.
The determinant of the given matrix is non zero. It is also constant. It does not depend on the value of x.
So, the A-1 exist for all real x.
Whenever we have to find the inverse of the matrix, we should check the determinant of the matrix. The determinant must be non zero for a inverse to exist.
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