List of top Mathematics Questions on types of matrices asked in KEAM

If $(x \;\; 3 \;\; -1)\begin{pmatrix} 1 & 1 & 1 \\ -1 & 0 & 1 \\ 1 & 0 & -1 \end{pmatrix}\begin{pmatrix} 2 \\ 3 \\ 1 \end{pmatrix} = 0$, then the values of $x$ are:

Let $P = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 10 & 100 & -1 \end{pmatrix}$. Then $P^{4052}$ is equal to:

If $A = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$ and $(\alpha I + \beta A)^2 = A$, where $I$ is $2 \times 2$ unit matrix, then $\alpha^2 - \beta^2 =$:

If \( \begin{pmatrix} -1 & 2 3 & -4 -5 & 6 \end{pmatrix} \begin{pmatrix} 7 8 \end{pmatrix} = \begin{pmatrix} \alpha \beta 13 \end{pmatrix} \), then the value of \( \alpha + \beta \) is equal to

If \( \begin{pmatrix} 3x-y & x+3y \\ 2x-z & 2y+z \end{pmatrix} = \begin{pmatrix} 7 & 9 \\ 5 & 5 \end{pmatrix} \), then \( x+y+z \) equals

Let \( A = \begin{pmatrix} \alpha & 0 \\ 1 & 1 \end{pmatrix} \) and \( B = \begin{pmatrix} 1 & 0\\ 5 & 1 \end{pmatrix} \) be two matrices where \( \alpha \) is a real number. Then

If \( A \) and \( B \) are two matrices such that \[ 3A + B = \begin{pmatrix} 9 & 11 & 3 \\ 12 & 14 & 19 \end{pmatrix} \] and \[ 2A - 3B = \begin{pmatrix} -16 & 11 & 2 \\ -3 & -22 & 9 \end{pmatrix}, \] then the matrix \( B \) is

If \( A = \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix} \), then \( A^n + nI \) is equal to:

If \( A = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \), then the value of \( A^{2017} \) is equal to:

If \( A = \begin{pmatrix} 1 & 5 \\ 0 & 2 \end{pmatrix} \), then which of the following equations is satisfied by matrix \( A \)?

If \( \begin{pmatrix} x+y & x-y \\ 2x+z & x+z \end{pmatrix} = \begin{pmatrix} 0 & 0 \\ 1 & 1 \end{pmatrix} \), then the values of \( x, y \) and \( z \) are respectively:

The value of \( \begin{pmatrix} 7 & 1 & 5 \\ 8 & 0 & 0 \end{pmatrix} \begin{pmatrix} 2 \\ 3 \\ 1 \end{pmatrix} + 5 \begin{pmatrix} 1 \\ 0 \end{pmatrix} \) is equal to:

Let \( A = \begin{bmatrix} 5 & 0 \\ 1 & 0 \end{bmatrix} \) and \( B = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \). If \( 4A + 5B - C = 0 \), then the matrix \( C \) is:

If the square of the matrix $\begin{pmatrix} a & b \\ a & -a \end{pmatrix}$ is the unit matrix, then $b$ is equal to:

Let \( A = \begin{bmatrix} 1 & \frac{-1-i\sqrt{3}}{2} \\ \frac{-1+i\sqrt{3}}{2} & 1 \end{bmatrix} \). Then \( A^{100} \) is equal to:

If \( \begin{bmatrix} 1 & x & 1 \end{bmatrix} \begin{bmatrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 2 & 0 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = 0 \), then the values of \( x \) are: