Algebra

Matrices & Determinants

Easy

common

If $A = \begin{bmatrix} 2 & 1 & -1 \\ 0 & 3 & -2 \\ k & 1 & 0 \end{bmatrix}$ is non-singular matrix, then the value(s) of $k$ belongs to:

[Where $R$ is the set of real numbers]

$R-\{0\}$

$R-\{4\}$

$R-\{-4\}$

$R$

✅ Correct Option: 3

Expanding along the first row:

$|A| = 2(0+2) - 1(0+2k) + (-1)(0-3k) = 4 - 2k + 3k = 4 + k$ .

A matrix is non-singular when $|A| \neq 0$ , so $4 + k \neq 0$ , i.e. $k \neq -4$ .

Hence $k \in R - \{-4\}$ .

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:

2023: 15 June Shift 2

If $\begin{bmatrix} 3 & 2x+5y & -2 \\ x+4y & 7 & -5 \end{bmatrix} = \begin{bmatrix} 3 & 10 & -2 \\ 2 & 7 & -5 \end{bmatrix}$ Then the values of $x$ and $y$ are :

2025: 21 May Shift 1

Let $A = [a_{ij}]_{3×2}$ and $B = [b_{ij}]_{3×4}$ be two matrices. Then the order of the matrix $(A^T . B)^T$ is:

2022: 25 May Shift 1

If A is a square matrix of order 3, B = kA and |B| = $x$ |A| then,

2026: 14 May Shift 2

If A is a 3x3 matrix then:

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert adj A\vert$	I.	$\vert A\vert^{-1}$
B.	$\vert A.adj A\vert$	II.	$\vert A\vert$
C.	$\vert A^{-1}\vert$	III.	$\vert A\vert^2$
D.	$\vert A^{-1}.adj A\vert$	IV.	$\vert A\vert^3$

Choose the correct answer from the options given below:

2025: 14 May Shift 1

If A and B are skew-symmetric matrices, then which one of the following is NOT true?

If A=[21−103−2k10]A = \begin{bmatrix} 2 & 1 & -1 \\ 0 & 3 & -2 \\ k & 1 & 0 \end{bmatrix}A=​20k​131​−1−20​​ is non-singular matrix, then the value(s) of kkk belongs to: [Where RRR is the set of real numbers]

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

If $A = \begin{bmatrix} 2 & 1 & -1 \\ 0 & 3 & -2 \\ k & 1 & 0 \end{bmatrix}$ is non-singular matrix, then the value(s) of $k$ belongs to:

[Where $R$ is the set of real numbers]