If A = bmatrix 3 & 7 \\ 4 & -2 bmatrix, X = bmatrix \\ -2 bmatrix, B = bmatrix 7 \\ 32 bmatrix and AX = B, then the value of the is Option 1: 7 Option 2: 4/3 Option 3: 1 Option 4: 5

Answer: 7. Solution: Given A = bmatrix 3 & 7 \\ 4 & -2 bmatrix, X = bmatrix \\ -2 bmatrix, B = bmatrix 7 \\ 32 bmatrix and AX = B. Calculate AX: AX = bmatrix 3 & 7 \\ 4 & -2 bmatrix bmatrix \\ -2 bmatrix For the first row: (3 x ) + (7 x -2) = 3 - 14 For the second row: (4 x ) + (-2 x -2) = 4 + 4 Therefore: AX = bmatrix 3 - 14 \\ 4 + 4 bmatrix Since AX = B: bmatrix 3 - 14 \\ 4 + 4 bmatrix = bmatrix 7 \\ 32 bmatrix This gives two equations: 3 - 14 = 7 4 + 4 = 32 Using the first equation: 3 - 14 = 7 3 = 21 = 7 Therefore, = 7

Algebra

Matrices & Determinants

Easy

applied

If $A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}$ , $X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}$ , $B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}$ and $AX = B$ , then the value of the $\alpha$ is

$7$

$\frac{4}{3}$

$1$

$5$

✅ Correct Option: 1

Given $A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}$ , $X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}$ , $B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}$ and $AX = B$ .

Calculate $AX$ :

$AX = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix} \begin{bmatrix} \alpha \\ -2 \end{bmatrix}$

For the first row:

$(3 \times \alpha) + (7 \times -2)$

$= 3\alpha - 14$

For the second row:

$(4 \times \alpha) + (-2 \times -2)$

$= 4\alpha + 4$

Therefore:

$AX = \begin{bmatrix} 3\alpha - 14 \\ 4\alpha + 4 \end{bmatrix}$

Since $AX = B$ :

$\begin{bmatrix} 3\alpha - 14 \\ 4\alpha + 4 \end{bmatrix} = \begin{bmatrix} 7 \\ 32 \end{bmatrix}$

This gives two equations:

$3\alpha - 14 = 7$

$4\alpha + 4 = 32$

Using the first equation:

$3\alpha - 14 = 7$

$3\alpha = 21$

$\alpha = 7$

Therefore, $\alpha = 7$

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: 13 May Shift 2

Let $\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ -8 & -4 \end{vmatrix}$ . Then

(A) $x = -4$

(B) $x = -6$

(D) $x = 6$

Choose the correct answer from the options given below:

2023: 30 May Shift 3

If order of matrix A is $m \times p$ and order of matrix B is $p \times n$ , then what is the order of matrix AB ?

2025: 19 May Shift 1

If matrix $A = \begin{bmatrix} p & -3 \\ -4 & p \end{bmatrix}$ and $|A^3| = 64$ , then the value of p is:

2023: 23 May Shift 3

The inverse of the matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ is:

2026: 31 May Shift 2

Let $A = \begin{bmatrix} 2 & 4 \\ -2 & 8 \end{bmatrix}$ . If $A^{-1} = \alpha I + \beta A$ , $\alpha,\beta \in R$ (Where R is set of real numbers) and I is a $2\times2$ identity matrix, than the value of $4(\alpha-2\beta)$ is equal to:

If A=[374−2]A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}A=[34​7−2​], X=[α−2]X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}X=[α−2​], B=[732]B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}B=[732​] and AX=BAX = BAX=B, then the value of the α\alphaα is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}$ , $X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}$ , $B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}$ and $AX = B$ , then the value of the $\alpha$ is