Question Library

Find the sum of the entries in the inverse of \(\begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}\)

If I is a 2 × 2 identity matrix, find the determinant of the matrix.

The determinant of the matrix \(A = \begin{pmatrix} -2 & 3 & 1 \\ p & 2 & 1 \\ 1 & 4 & 2\end{pmatrix}\) is -5. Find the value of p.

Given that \(P = \begin{pmatrix} 1 & 3 \\ 2 & -5 \end{pmatrix}\) and Q = \(\begin{pmatrix} 3 & -7 \\ 1 & 2 \end{pmatrix}\) . Find P + 2Q

Evaluate the determinant of the matrix M = \(\begin{bmatrix}3 & 4 & 6\\2 & 1 & -1\\-1 & 3 & 5\end{bmatrix}\)

Let A = \(\begin{pmatrix}2 & -4 & 3\\5 & 1 & 0\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4 & -2\\-3 & 3 & -1\end{pmatrix}\). Find A + 2B

If A = \(\begin{pmatrix}3 & 2 & 1\\4 & 2 & -1\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4\\0 & 1\\3 & 2\end{pmatrix}\). Find A\(^T\) + B, ( where T means transpose)

If D = \(\begin{bmatrix}2& -1&3\\4&1&2\\1&-3&1\\\end{bmatrix}\) Find |D|

Find the matrix A A \(\begin {bmatrix} 0 & 1\\2 & -1 \end {bmatrix}\) = \(\begin {bmatrix} 2 & -1\\1 & 0 \end {bmatrix}\)

Find the determinant of the matrix A = \(\begin{pmatrix} 2 & 3 \\ 1 & 3 \end{pmatrix}\)

A matrix P \(\begin{pmatrix}a & b\\ c & d\end{pmatrix}\) is such that P\(^T\) = - P, where P\(^T\) is the transpose of P. If b = 1, then P is

Find the values of t for which the determinant of the matrix \(\begin{pmatrix}t-4 & 0 & 0\\ -1 & t+1 & 1\\3 & 4 & t-2\end{pmatrix}\) is zero.