List of top Mathematics Questions on Matrices asked in KEAM

Suppose \(A=\begin{bmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{bmatrix}\) is an adjoint of the matrix \(\begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{bmatrix}\). Then the value of \(\frac{a_!+b_2+c_3}{b_1a_2}\) is

Let A be (2n+1)×(2n+1) matrix with integer entries and positive determinant,where n∈N.If AA^T = I = A^TA, then which of the following statements always holds?

If A=[2 0 6] and \(B=\begin{bmatrix} 3&\ \ 5\\7&-2\\6&\ \ 6 \end{bmatrix}\), then AB=

If A is non-singular matrix and if \(A^{-1}=\frac{1}{2}\begin{bmatrix} -10&-4\\2&1\end{bmatrix}\), then adj(A)=

Let \(A= \begin{bmatrix} 3&4\\ 1&-2 \end{bmatrix}\) and let \(AB= \begin{bmatrix} -5&41\\ 5&-13 \end{bmatrix}\). Then |B^T| =

The matrix \(\begin{bmatrix} -2&1&0\\3&4&1\\-4&\lambda&0 \end{bmatrix}\) is non-singular for \(\lambda\ne\)

If \(AB=\begin{bmatrix} 4&3\\5&4 \end{bmatrix}\) and \(A^{-1}=\begin{bmatrix} 3&-2\\-1&1 \end{bmatrix}\), then B=

Let \(A+B=\begin{bmatrix} 4&1&4\\1&4&4 \end{bmatrix}\)and \(B=\begin{bmatrix} 1&0&-2\\-1&3&0 \end{bmatrix}\), then A=

If \( A = \begin{bmatrix} 2-k & 2 \\ 1 & 3-k \end{bmatrix} \) is a singular matrix, then the value of \( 5k - k^2 \) is equal to:

If \( A = \begin{bmatrix} 2-k & 2 \\ 1 & 3-k \end{bmatrix} \) is a singular matrix, then the value of \( 5k - k^2 \) is equal to:

If \( A = \begin{bmatrix} 2-k & 2 \\ 1 & 3-k \end{bmatrix} \) is a singular matrix, then the value of \( 5k - k^2 \) is equal to:

If $ A= \begin{bmatrix} 1 & 0 & 0 \\ x & 1 & 0 \\ x & x & 1 \\ \end{bmatrix} $ and $ I= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} , $ then $ {{A}^{3}}-4{{A}^{2}}+3A+I $ is equal to

If $A$ and $B$ are square matrices of the same order and if $A=A^{T},B=B^{T},$ then $\left(ABA\right)^{T}=$

If $\begin{pmatrix}2x+y&x+y\\ p-q&p+q\end{pmatrix}=\begin{pmatrix}1&1\\ 0&0\end{pmatrix}$ , then $(x, y, p, q) $ equals

If \(\begin{bmatrix}e^{x}&e^{y}\\ e^{y}&e^{x}\end{bmatrix} = \begin{bmatrix}1&1\\ 1&1\end{bmatrix}\), then the values of \(x\) and \(y\) are respectively:

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

If $A = \begin{pmatrix}1&5\\ 0&2\end{pmatrix}$ , then

If $ A= \begin{bmatrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \\ \end{bmatrix} , $ then $ {{A}^{4}} $ is equal to