List of practice Questions

Let $AX=B$ be a system of n-linear equations in n unknowns then
Let \(A\) be a \(2\times2\) real symmetric matrix such that the trace of \(A\) is \(6\) and the determinant of \(A\) is \(5\). Which one of the following statements is true?
If a $3 \times 3$ matrix $A$ has eigenvalues $2, 3, -4$, find $\det(A)$.
Find the inverse of the given matrix: \[ A = \begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix} \]

The sum of the eigenvalues of the matrix 
\( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}^2 \) 
is _____________ (rounded off to the nearest integer). 

If $M$ is an arbitrary real $n \times n$ matrix, then which of the following matrices will have non-negative eigenvalues?

For the matrix \[ [A] = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 2 & 1 \\ 3 & 1 & 2 \end{bmatrix} \] which of the following statements is/are TRUE?