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

The value (/s) of $x$ satisfying the matrix equation:

$x\begin{bmatrix}2x & 2\\3 & x\end{bmatrix}+2\begin{bmatrix}8 & 5x\\4 & 4x\end{bmatrix}=2\begin{bmatrix}(x^2+8) & 24\\10 & 6x\end{bmatrix}$ is/are:

Let A, B be square matrices of order $3\times3$. Then $|A.adj(A).B|$ is

If A and B are two symmetric matrices of the same order, then

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Let $A=\begin{bmatrix}1 & \sin\theta & 1\\-\sin\theta & 1 & \sin\theta\\-1 & -\sin\theta & 1\end{bmatrix}$, where $\theta\in[0,2\pi]$ then which of the following statements are correct?

A. $|A|=2+2\sin^2\theta$

B. Maximum value of $|A|$ is 1.

C. Maximum value of $|A|$ is –1.

D. $|A|\in[2,4]$

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The value of the determinant $\Delta=\begin{vmatrix}\cos\alpha\cos\beta & \cos\alpha\sin\beta & -\sin\alpha\\-\sin\beta & \cos\beta & 0\\\sin\alpha\cos\beta & \sin\alpha\sin\beta & \cos\alpha\end{vmatrix}$ is:

If $A=\begin{bmatrix}2 & 3\\1 & 2\end{bmatrix}, I=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ and $A^2=\alpha A+\beta I$, for some constant $\alpha$ and $\beta$ then the value of $\alpha$ and $\beta$ respectively:

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The value of $\begin{vmatrix}1 & \log_ba\\\log_ab & 1\end{vmatrix}$ is:

If $A=\begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$ and $f(x)=x^2-2x-3$, then $f(A)$ is equal to

If $A$ is a square matrix of order 3 and $|A|=6$, then the value of $|2A^T|$ is:

If $A$ is a square matrix of order 3 such that $A(adj\,A)=\begin{bmatrix}-3 & 0 & 0\\0 & -3 & 0\\0 & 0 & -3\end{bmatrix}$, then which of the following is NOT correct?

If the matrix $\begin{bmatrix}0 & \alpha & 2\\2 & \beta & 1\\\gamma & -1 & 0\end{bmatrix}$ is skew-symmetric, then $(\beta-\alpha-\gamma)$ equals

Which of the following statements are correct?

A. If $P$ and $Q$ are square matrices of same order, then $(PQ^T-QP^T)$ is a skew symmetric matrix.

B. The number of all possible matrices of order $3\times2$ with each entry either –1 or 1, is 64.

C. If $P$ is an invertible matrix, then $P^T$ is also invertible.

D. If $P$ and $Q$ are square matrices of the same order, then $|PQ|=|P|+|Q|$.

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For what values of $\lambda$ and $\mu$, the following system of linear equations:

$x+y+2z=1, 2x+y-z=4, x+2y+\lambda z=\mu$

have infinitely many solution?

If the matrix $A = \begin{bmatrix} -2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ is given, then which of the following statements is/are TRUE?

A. A is a square matrix

B. A is a symmetric matrix

C. A is a scalar matrix

D. A is a identity matrix

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

If A is a diagonal matrix of order 3 with diagonal elements as 2, 3, 4, then |adj A| is

If area of the triangle formed by A(1, 3), B(0, 0) and C(k, 0) is 3 sq. units, then which of the following is/are TRUE?

A. k = 2

B. k = -2

C. k = 3

D. k = -3

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If A and B are square matrices of order 3×3 such that |A|=7 and |B|=6, then |B adj A| =

If $A=\begin{bmatrix}1&1&1\\1&0&2\\3&1&1\end{bmatrix}$ and $B=\begin{bmatrix}-2&0&2\\5&-2&-1\\1&2&-1\end{bmatrix}$ such that AB=4I (where I is identity matrix) then solution of system of equations $x+y+z=6, x+2z=7, 3x+y+z=12$ is

If $\begin{vmatrix}2a & 2a & 3b+c\\3b & 2a+c & 3b\\2a+3b & c & c\end{vmatrix} = 48$, then abc is equal to

If $\begin{vmatrix}x&2\\18&x\end{vmatrix} = \begin{vmatrix}6&2\\18&6\end{vmatrix}$, then x equals:

Let $A=[a_{ij}]_{3\times3}$, where $a_{ij}=i-j$, then which of the following statements is/are TRUE ?

A. A is diagonal matrix

B. A is square matrix

C. A is symmetric matrix

D. A is skew symmetric matrix

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If A is a skew symmetric matrix, then $A^2$ is a

The determinant of which of the following matrices is a perfect square ?

A. $\begin{bmatrix}5&29\\-1&6\end{bmatrix}$

B. $\begin{bmatrix}5&26\\1&6\end{bmatrix}$

C. $\begin{bmatrix}10&3\\17&10\end{bmatrix}$

D. $\begin{bmatrix}8&5\\-3&-8\end{bmatrix}$

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With reference to the matrix $A=\begin{bmatrix}5&0&0\\0&5&0\\0&0&-5\end{bmatrix}$, which of the following are TRUE ?

A. |A|=125

B. A is a scalar matrix.

C. A is a diagonal matrix.

D. |A|=-125

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If matrix $A=\begin{bmatrix}0&3a&-4\\2&1&2\\2b&2&-1\end{bmatrix}$ is a symmetric matrix, then the values of $a$ and $b$ are

Given that $[a_{ij}]$ is a square matrix of order n.

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