List of top Engineering Mathematics Questions on Matrices asked in TS PGECET

The system of equations \[ x+4y+6z=20,\qquad x+y+z=6,\qquad x+\lambda y+6z=20 \] has

Let \(A\) be a real symmetric matrix. \(\lambda_1,\lambda_2\;(\lambda_1\neq\lambda_2)\) be two eigen values of \(A\) and \(X_1,X_2\) are respectively the eigen vectors of \(A\) corresponding to \(\lambda_1\) and \(\lambda_2\), then \(X_1^TX_2=\)

\[ \lim_{n\rightarrow\infty}\frac{5n^{2}+4}{7n^{2}+6n}= \]

If \[ f(x,y,z,w)=x^{2}e^{2y+3z}\cos(4w), \] then \[ \frac{\partial f}{\partial z} \] at \((2,0,-2,1)\) is

If \[ \begin{bmatrix} 1 1 \end{bmatrix} \] is an eigenvector of the matrix \[ A= \begin{bmatrix} m& 3 \\ 3& m \end{bmatrix}, \] then the corresponding eigenvalue is:

The system of equations \[ x-2y+3z=6,\quad 3x+y-4z=-7,\quad 5x-3y+2z=5 \] has:

Which of the following cannot be an eigen value for an unitary matrix?

If \(A\) is symmetric, \(P\) and \(B\) are skew symmetric matrices, then which of the following is correct?

Let \(A=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}\). If \(u_1\) and \(u_2\) are column matrices such that \(Au_1 = \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix}\) and \(Au_2 = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}\), then \(u_1 - u_2\) is