List of top Mechanical Engineering Questions on Linear Algebra asked in CUET (PG)

If \( A = \begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix} \) satisfies the matrix polynomial equation \( A^2 - 4 + kI_2 = 0 \), then determine the value of \( k \).

The solution of the following system of linear equations
\(4x_1 - 8x_2 - 2x_3 = 0\)
\(3x_1 - 5x_2 - 2x_3 = 0\) 
\(2x_1 - 8x_2 + x_3 = 0\) is:

The eigenvalues of the matrix
\[ \begin{bmatrix} 1 & -2 & 3 \\ -2 & 2 & -4 \\ 3 & -4 & 7 \end{bmatrix} \] are: