List of top Mathematics Questions on Matrix asked in CBSE CLASS XII

Three students run on a racing track such that their speeds add up to 6 km/h. However, double the speed of the third runner added to the speed of the first results in 7 km/h. If thrice the speed of the first runner is added to the original speeds of the other two, the result is 12 km/h. Using the matrix method, find the original speed of each runner.

Find the value of $x$, if \[ \begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ x \\ 2 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \]

If the matrix \[ \begin{bmatrix} 1 & 12 & 4y \\ 6x & 5 & 2x \\ 8x & 4 & 6 \end{bmatrix} \]
is a symmetric matrix, then the value of \( 2x + y \) is:

If \( A = \begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix} \), then find the value of \( K \) if \( A^2 = 6A + K I_2 \), where \( I_2 \) is the identity matrix.

If \( A \) and \( B \) are two non-zero square matrices of the same order such that \[ (A + B)^2 = A^2 + B^2, \] then:

The determinant \(\begin{vmatrix} x+1 & x-1 \\ x^2+x+1 & x^2-x+1 \end{vmatrix}\) is equal to:

Let \[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \] be a square matrix such that \[ \text{adj } A = A. \] Then, \( (a + b + c + d) \) is equal to:

If \[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix}, \] then \( A^{-1} \) is:

If \[ \begin{bmatrix} 1 & 3 & 1 \\ k & 0 & 1 \\ 1 & 0 & 1 \end{bmatrix} \] has a determinant of \( \pm 6 \), then the value of \( k \) is:

The value of \[ \begin{vmatrix} 8 & 2 & 7 \\ 12 & 3 & 5 \\ 16 & 4 & 3 \end{vmatrix} \textbf{is:} \]

If \( A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix} \), then \( A^{-1} \) is:

If \( A = [a_{ij}] \) is an identity matrix, then which of the following is true?

Given that \[ \begin{bmatrix} 1 & x \end{bmatrix} \begin{bmatrix} 4 & 0 \\ -2 & 0 \end{bmatrix} = 0 \] then the value of \( x \) is:

Let \( \Delta = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) be a square matrix such that \( \text{adj} A = A \). Then, \( (a + b + c + d) \) is equal to:

If \( A = \begin{bmatrix} 2 & 1 \\ -4 & -2 \end{bmatrix} \), then the value of \( I - A + A^2 - A^3 + \dots \) is:

If \[ \begin{bmatrix} a & c & 0 \\ b & d & 0 \\ 0 & 0 & 5 \end{bmatrix} \] is a scalar matrix, then the value of \[ a + 2b + 3c + 4d \] is:

Given matrix:
Let \[ A = \begin{bmatrix} 2 & 1 & -3 \\ 3 & 2 & 1 \\ 1 & 2 & -1 \end{bmatrix} \] Find \( A^{-1} \) and hence solve the following system of equations:

System of equations:
\[ 2x + y - 3z = 13, \quad 3x + 2y + z = 4, \quad x + 2y - z = 8 \]