Question

Let \( A = \begin{pmatrix} 1 & 3 & 2 \\ 4 & 2 & 5 \\ 7 & -t & -6 \end{pmatrix} \), then the values of \( t \) for which inverse of \( A \) does not exist are:

• A. 2, 1
• B. 3, 2
• C. 2, -1
• D. 3, 1

Hint:

For a matrix to be invertible, its determinant must be non-zero. Set the determinant equal to zero to find when the matrix is non-invertible.

Answer 1

The Correct Option is C

Step 1: Inverse of matrix condition. The inverse of a matrix does not exist if its determinant is zero. To find the values of \( t \), we calculate the determinant of matrix \( A \) and solve for \( t \) when the determinant equals zero.
Step 2: Conclusion. Thus, for values \( t = 2 \) and \( t = -1 \), the inverse of \( A \) does not exist.