Algebra

Matrices & Determinants

Medium

core

If $\begin{bmatrix} x-2 & 3 & y \\ -3 & 0 & 2 \\ 4 & z-1 & 0 \end{bmatrix}$ is a skew-symmetric matrix, then the value of $x+y+z$ is:

-1

-3

✅ Correct Option: 2

For a skew-symmetric matrix the diagonal entries are zero and $a_{ij} = -a_{ji}$ .

Diagonal: $x-2 = 0 \Rightarrow x = 2$ .

From $a_{13} = -a_{31}$ : $y = -4$ .

From $a_{32} = -a_{23}$ : $z-1 = -2 \Rightarrow z = -1$ .

So $x+y+z = 2-4-1 = -3$ .

2025: 30 May Shift 2

The diagonal elements of a skew symmetric matrix are all

2026: 22 May Shift 1

For every square matrix $A$ of order $n\times n$ , which of the following statements are correct ?

(A) $(adjA)A = A(adjA) = |A|I$ , where $I$ is identity matrix of order n.

(B) $|kA|=k^n|A|$ , k is any scalar.

(D) $A^2=A$

Choose the correct answer from the options given below:

2026: 18 May Shift 2

If $A=\begin{bmatrix} 2 & 1 \\ 7 & 5 \end{bmatrix}$ , then the value of $|A(adj A)|$ is

2023: 30 May Shift 3

If matrix $A = \begin{bmatrix} 3 & x \\ y & 0 \end{bmatrix}$ and $A' = A$ , then :

2026: 29 May Shift 1

If A is a non-singular matrix of order 3, then

Match List-I with List-II

List-I	List-II
Determinant of A	$\left\vert \text{adj}(\text{adj } A) \right\vert =$
(A) $\left\vert A \right\vert = 3$	(I) $1$
(B) $\left\vert A \right\vert = 4$	(II) $16$
(C) $\left\vert A \right\vert = 2$	(III) $81$
(D) $\left\vert A \right\vert = 1$	(IV) $256$

Choose the correct answer from the options given below:

2025: 27 May Shift 1

The following system of equations:

$x + y - z = 7$

$4x + \lambda y - \lambda z = 3$

$3x + 2y - 4z = 5$

does not possess a solution if the value of $\lambda$ is:

If [x−23y−3024z−10]\begin{bmatrix} x-2 & 3 & y \\ -3 & 0 & 2 \\ 4 & z-1 & 0 \end{bmatrix}​x−2−34​30z−1​y20​​ is a skew-symmetric matrix, then the value of x+y+zx+y+zx+y+z is: