List of top Mathematics Questions on Matrices asked in CUET (PG)

If $A=\begin{bmatrix} 7 & 9 & -2 \\ -2 & 0 & 3 \end{bmatrix}$ and $B=\begin{bmatrix} 1 & 0 & 5 \\ 6 & 3 & 2 \end{bmatrix}$ then A+B =

The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?

If the matrices $\left(\begin{matrix} 1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   -1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   i & 0 \\   0 & 0  \end{matrix}\right) and \left(\begin{matrix}   -i & 0 \\   0 & 0  \end{matrix}\right)$ form a group with respect to matrix multiplication, then which one of the following statements about the groups, thus formed is correct?

Consider the linear mapping F: R² →R² defined by F(x, y) = (3x+4y, 2x-5y) and following bases of R²: E= {e₁, e₂} = {(1, 0), (0, 1)} and S = {u₁, u₂} = {(1, 2), (2, 3)}. Then the matrix A representing F relative to the basis E is:

If λ₁,λ₂,λ₃ are the given values of the matrix $\begin{bmatrix}   -2 & 2 & -3 \\   2 & 1 & -6 \\ -1 & -2 & 0 \end{bmatrix}$, then λ₁²+λ₂²+λ₃² is equal to

The dimension of the general solution space W of the homogeneous system
x₁+2x₂-3x₃+2x₄-4x₅=0
2x₁+4x₂-5x₃+x₄-6x₅ = 0
5x₁+10x₂-13x₃+4x₄-16x₅= 0

Let F: R³ →R² be the linear map defined by F(x, y, z) = (3x+2y-4z, x-5y+3z). The basis of R³ is S and basis of R² is S', where S = {(1, 1, 1), (1, 1, 0), (1, 0, 0)} and S' = {(1, 3), (2, 5)}. Then the matrix of F in the bases of R³ and R² is

If A=$\begin{bmatrix} 1 & 2 & 0 & -1\\   2 & 6 & -3 & -3\\  3 & 10 & -6 & -5 \end{bmatrix}$, then which one of the following is true?

The rank of matrix A = $\begin{bmatrix} 1&3&1&-2&-3\\1&4&3&-1&-4\\2&3&-4&-7&-3\\3&8&1&-7&-8 \end{bmatrix}$

Let A =$\begin{bmatrix}2&3\\4&-1\end{bmatrix}$ then the matrix B that represents the linear operator A relative to the basis
S = {$u_1,u_2$}=${[1, 3]^T, [2, 5]^T}$, is:

Which one of the following is a cyclic group?

Let A and B be 2 × 2 matrices, then which of the following is correct?

If A is symmetric real valued matrix of dimension 2022, then eigenvalues of A are