CUET Mathematics: AlgebraMatrices & Determinants. Free, no login required.

If the matrix $\begin{bmatrix}3 & 2a & -5\\4 & 0 & b\\-5 & 3 & 10\end{bmatrix}$ is symmetric, then the value of $5a + 2b$ is

If $A$ is a square matrix of order 3 and $|A| = 5$, then the value of $|-AA^T|$ is

If the matrix $\begin{bmatrix}2 & -1 & 3\\ \lambda & 0 & 7\\-1 & 1 & 4\end{bmatrix}$ is not invertible, then value of $\lambda$ is

if $A = \begin{bmatrix}1 & 0\\3 & 1\end{bmatrix}$ and $A^4 = \begin{bmatrix}1 & 0\\k & 1\end{bmatrix}$ then value of $k$ is

If $A$ is a skew-symmetric matrix of order 5, then $|adjA|$ is equal to

If $x, y$ and $z$ are real number such that $x + y + z = 0$, then value of $\begin{vmatrix}3x & -x+y & -x+z\\x-y & 3y & z-y\\x-z & y-z & 3z\end{vmatrix}$ is

If $A$ is an invertible matrix of order 3, then

Match List-I with List-II

Choose the correct answer from the options given below:

The matrix $A = \begin{bmatrix}0 & 0 & 5\\0 & 5 & 0\\5 & 0 & 0\end{bmatrix}$ is a

(A) Diagonal matrix

(B) Scalar matrix

(C) Square matrix

(D) Symmetric matrix

Choose the correct answer from the options given below:

If A is a square matrix such that $A^2=A$ and I is the identify matrix of the same order as A then $(I + 2A)^3$-6A is equal to

If $A = \begin{bmatrix}0 & x^2-6 & -3\\-x & 0 & -8\\x^2-2x & 8 & 0\end{bmatrix}$ is a skew symmetric matrix, then the value(s) of x is/ are -

(A) 3

(B) -3

(C) -2

(D) -1

Choose the correct answer from the options given below:

If $A = \begin{bmatrix}1 & 2\\ 0 & 3\end{bmatrix}$ then $|A. adj A|$ is

Which of the given values of $x$ and $y$ make the following pair of matrices equal ?

$\begin{bmatrix}2x-1 & 4\\y-1 & 3+2x\end{bmatrix}$ and $\begin{bmatrix}0 & y-2\\5 & 4\end{bmatrix}$

If $a_{ij}=i+3j$, then the matrix of order 2 with elements as $a_{ij}$ is

Given a matrix A of order 3x3. If |A|=3 then the value of |A(adj A)| is:

The value of $\begin{vmatrix} x^2 - x + 1 & x - 1 \\ x + 1 & x + 1 \end{vmatrix}$ is equal to:

If $\begin{bmatrix}2x+1 & 5x \\ 0 & y^2+1\end{bmatrix} = \begin{bmatrix}x+3 & 10 \\ 0 & 26\end{bmatrix}$ then the possible values of x + y are:

If $A = \begin{bmatrix}1 & -1 \\ 2 & -1\end{bmatrix}$, $B = \begin{bmatrix}a & 1 \\ b & -1\end{bmatrix}$ and $(A + B)^2 = A^2 + B^2$ then

If $x, y, z$ are non-zero numbers, then the inverse of matrix $A = \begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}$ is

The diagonal elements of a skew symmetric matrix are all

If $A = [a_{ij}]_{3 \times 2}$ where $a_{ij} = i + j$, then

(A) A is a square matrix

(B) $a_{21} + a_{32} = 8$

(C) Number of elements in A is 6

(D) Transpose of $A = \begin{bmatrix}2 & 3 \\ 3 & 4 \\ 4 & 5\end{bmatrix}$

Choose the correct answer from the options given below:

If A is a singular matrix, then A{adj A} is equal to

The value of $\begin{vmatrix}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{vmatrix}$ is

If the system of equations

$x - 3y + 5z = 3$

$x - 2y + 4z = 4$

$2x - 7y + \lambda z = 5$

has infinite number of solutions, then the value of $\lambda$ is:

If $x = -4$ is a root of $\begin{vmatrix}x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x\end{vmatrix} = 0$, then the sum of the other 2 roots is

The minimum value of $\begin{vmatrix}2 & 2 & 2 \\ 2 & 2+x & 2 \\ 2 & 2 & 2+x\end{vmatrix}$, $x \in R$ is

If $A = \begin{bmatrix}2 & 3 & 1 \\ 2 & -1 & 0\end{bmatrix}$ and $B^T = \begin{bmatrix}4 & 4 \\ 6 & -2 \\ 2 & 0\end{bmatrix}$, then $4A + B$ is

Let $A$ and $B$ be square matrices of order 3, then det $[(A - A^T) + (B - B^T)]$ is equal to

Which of the following statement('s) is/are TRUE?

(A) Skew symmetric matrix of even order is always symmetric

(B) Skew symmetric matrix of odd order is non-singular

(C) Skew symmetric matrix of odd order is singular

(D) Skew symmetric matrix is always square matrix

Choose the correct answer from the options given below:

If A is a square matrix and I is the identity matrix of same order such that $A^2 = I$, then $3(A - I)^3 + 3(A + I)^3 - 15A$ is equal to

If $A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 2 \\ 2 & 0 \end{bmatrix}$, then the matrix AB is equal to