If pmatrix 2x & 5 \\ 8 & x pmatrix = pmatrix 6 & -2 \\ 1 & 1 pmatrix, then the value of x is Option 1: ±2√6 Option 2: ±6√2 Option 3: ±√6 Option 4: √6

Answer: ±2√6. Solution: For any 2 x 2 matrix pmatrix a & b \\ c & d pmatrix, the determinant is ad - bc. Determinant of the left-hand side: pmatrix 2x & 5 \\ 8 & x pmatrix = (2x)(x) - (5)(8) = 2x^2 - 40 Determinant of the right-hand side: pmatrix 6 & -2 \\ 1 & 1 pmatrix = (6)(1) - (-2)(1) = 6 + 2 = 8 Note: subtracting a negative means we add, so 6 - (-2) = 6 + 2. Setting the two determinants equal: 2x^2 - 40 = 8 2x^2 = 48 x^2 = 24 x = ±√24 Simplifying: √24 = √(4 x 6) = 2√6 x = ± 2√6

Algebra

Matrices & Determinants

Medium

core

If $\det \begin{pmatrix} 2x & 5 \\ 8 & x \end{pmatrix} = \det \begin{pmatrix} 6 & -2 \\ 1 & 1 \end{pmatrix}$ , then the value of $x$ is

$±2\sqrt{6}$

$±6\sqrt{2}$

$±\sqrt{6}$

$\sqrt{6}$

✅ Correct Option: 1

For any $2 \times 2$ matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ , the determinant is $ad - bc$ .

Determinant of the left-hand side:

$\det \begin{pmatrix} 2x & 5 \\ 8 & x \end{pmatrix} = (2x)(x) - (5)(8) = 2x^2 - 40$

Determinant of the right-hand side:

$\det \begin{pmatrix} 6 & -2 \\ 1 & 1 \end{pmatrix} = (6)(1) - (-2)(1) = 6 + 2 = 8$

Note: subtracting a negative means we add, so $6 - (-2) = 6 + 2$ .

Setting the two determinants equal:

$2x^2 - 40 = 8$

$2x^2 = 48$

$x^2 = 24$

$x = \pm\sqrt{24}$

Simplifying: $\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}$

$\boxed{x = \pm\, 2\sqrt{6}}$

2023: 15 June Shift 2

The value of $\begin{vmatrix} \sqrt{3}/2 & 1/2 \\ \sqrt{3}/2 & 1/2 \end{vmatrix}$

2022: 10 Aug Shift 1

The length of the plot is:

2026: 15 May Shift 1

If $\begin{vmatrix} x-2 & -3 \\ 3x & 2x \end{vmatrix} = 3$ , then the values of $x$ are:

2026: 29 May Shift 1

Let $A=[a_{ij}]$ be a matrix of order $3 \times 4$ such that $a_{ij}=\begin{cases}2i-3j, & i \ge j \\ 3i+j, & i<j\end{cases}$ then the sum of all the elements of the first two rows of this matrix is:

2026: 22 May Shift 1

If $A=\begin{bmatrix}1 & 1 & 1\\1 & 0 & 3\\1 & -2 & 1\end{bmatrix}$ , then

Match List-I with List-II

List-I	List-II
(A) $\lvert A\rvert$	(I) 48
(B) $\lvert 2A\rvert$	(II) 36
(C) $\left\lvert\operatorname{adj}(A)\right\rvert$	(III) 12
(D) $2\lvert A\rvert$	(IV) 6

Choose the correct answer from the options given below:

2025: 13 May Shift 2

Let $A = \begin{bmatrix} 2 & -3 & 4 \\ 0 & 1 & 5 \\ -4 & 2 & 3 \end{bmatrix}$ and $a_{ij}$ be any element of matrix A, i, j ∈ {1,2,3}, then which of the following are TRUE?

(A) Minor of $a_{23} = 16$

(B) Minor of $a_{23} = -8$

(D) Cofactor of $a_{23} = 8$

(E) Cofactor of $a_{13} = 4$

Choose the correct answer from the options given below:

If det⁡(2x58x)=det⁡(6−211)\det \begin{pmatrix} 2x & 5 \\ 8 & x \end{pmatrix} = \det \begin{pmatrix} 6 & -2 \\ 1 & 1 \end{pmatrix}det(2x8​5x​)=det(61​−21​), then the value of xxx is

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CUET Mathematics Past Year Questions (Topic-Wise)

If $\det \begin{pmatrix} 2x & 5 \\ 8 & x \end{pmatrix} = \det \begin{pmatrix} 6 & -2 \\ 1 & 1 \end{pmatrix}$ , then the value of $x$ is