Algebra

Matrices & Determinants

Medium

applied

If the matrix $A = \begin{bmatrix} x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0 \end{bmatrix}$ is skew-symmetric, then the value of $2x - 3y + 5z$ is equal to

-10

-18

✅ Correct Option: 4

A skew-symmetric matrix is one where the transpose equals the negative of the original matrix. This means:

All diagonal elements must be 0
Mirror elements across the diagonal are negatives of each other

Given matrix:

$A = \begin{bmatrix} x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0 \end{bmatrix}$

The diagonal elements are $x$ , $0$ , and $0$ .

Since all diagonal elements must be 0:

$x = 0$

For mirror elements across the diagonal to be negatives of each other:

Position $(1,2)$ and $(2,1)$ :

Element at row 1, column 2 is $2$

Element at row 2, column 1 is $-2$

This satisfies $2 = -(-2)$ ✓

Position $(1,3)$ and $(3,1)$ :

Element at row 1, column 3 is $y$

Element at row 3, column 1 is $-1$

For skew-symmetric: $y = -(-1)$

$y = 1$

Position $(2,3)$ and $(3,2)$ :

Element at row 2, column 3 is $3$

Element at row 3, column 2 is $z$

For skew-symmetric: $3 = -z$

$z = -3$

The values are:

$x = 0$
$y = 1$
$z = -3$

Substituting into $2x - 3y + 5z$ :

$2x - 3y + 5z = 2(0) - 3(1) + 5(-3)$

$= 0 - 3 - 15$

$= -18$

Therefore, the value of $2x - 3y + 5z$ is $-18$ .

2025: 13 May Shift 2

Let A, B, C, D and E be matrices of order $2 \times n, 3 \times k, 2\times p, n \times 3$ and $p \times k$ respectively. Choose the correct statement(s) from the following?

(A) EB + DB will be defined if $k = 3, p = n$ .

(B) EB + DB will be defined if $k = 2, p = 3$ .

(D) If n = p, then the order of the matrix $5A^2 - 3C$ is $p \times k$ .

Choose the correct answer from the options given below:

2025: 3 June Shift 2

If A and B are symmetric matrices, then AB - BA is

2022: 7 Aug Shift 2

Match List - I with List - II.

	List - I		List - II
(A)	$A = \begin{bmatrix} 6 & 9 \\ 2 & 3 \end{bmatrix}$ , $B = \begin{bmatrix} 2 & 6 & 0 \\ 7 & 9 & 8 \end{bmatrix}$ , AB will be	(I)	$\begin{bmatrix} 75 & 117 & 72 \\ 35 & 39 & 24 \end{bmatrix}$
(B)	$P = \begin{bmatrix} 8 & 45 & 30 \\ 17 & 19 & 5 \end{bmatrix}$ , $Q = \begin{bmatrix} 67 & 72 & 42 \\ 8 & 30 & 19 \end{bmatrix}$ , P+Q will be	(II)	$\begin{bmatrix} 75 & 117 & 72 \\ 25 & 39 & 24 \end{bmatrix}$
(C)	$\begin{bmatrix} 85 & 42 & 69 \\ 73 & 42 & 50 \end{bmatrix} - \begin{bmatrix} 10 & -75 & -3 \\ 38 & 3 & 26 \end{bmatrix}$	(III)	$\begin{bmatrix} 75 & 117 & 72 \\ 25 & 49 & 24 \end{bmatrix}$
(D)	$2 \begin{bmatrix} 34 & 36 & 30 \\ 12 & 18 & 20 \end{bmatrix} + \begin{bmatrix} 7 & 55 & 12 \\ 1 & 13 & -16 \end{bmatrix}$	(IV)	$\begin{bmatrix} 75 & 127 & 72 \\ 25 & 49 & 24 \end{bmatrix}$

Choose the correct answer from the options given below :

2026: 29 May Shift 2

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

Choose the correct answer from the options given below:

2025: 26 May Shift 2

The value of $\begin{vmatrix} 2^x & 1 & 6^x \\ 4^x & 1 & 3^x \\ 2^x & 1 & 6^x \end{vmatrix}$ , where $x \neq 0$ is:

2026: 25 May Shift 1

If $P = \dfrac{1}{14}\begin{bmatrix} 3 & 2 \\ -4 & 2 \end{bmatrix}$ and $P^{-1} = \begin{bmatrix} x & -2 \\ 4 & y \end{bmatrix}$ , then the value of $x$ and $y$ respectively are

If the matrix A=[x2y−203−1z0]A = \begin{bmatrix} x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0 \end{bmatrix}A=​x−2−1​20z​y30​​ is skew-symmetric, then the value of 2x−3y+5z2x - 3y + 5z2x−3y+5z is equal to

Solution

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Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

If the matrix $A = \begin{bmatrix} x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0 \end{bmatrix}$ is skew-symmetric, then the value of $2x - 3y + 5z$ is equal to