If bmatrix x+y & 4 \\ 1+z & y bmatrix = bmatrix 2 & 4 \\ 5 & 6 bmatrix, then Option 1: x = 4, y = -6, z = 4 Option 2: x = -4, y = 6, z = 4 Option 3: x = -4, y = 6, z = -4 Option 4: x = 4, y = -6, z = -4

Answer: x = -4, y = 6, z = 4. Solution: Two matrices are equal when each element in the first matrix equals the corresponding element in the same position in the second matrix. bmatrix x+y & 4 \\ 1+z & y bmatrix = bmatrix 2 & 4 \\ 5 & 6 bmatrix Comparing corresponding positions: Top-left: x + y = 2 ... (1) Top-right: 4 = 4 ✓ Bottom-left: 1 + z = 5 ... (2) Bottom-right: y = 6 ... (3) From equation (3): y = 6 From equation (2): 1 + z = 5 z = 5 - 1 z = 4 From equation (1), substituting y = 6: x + 6 = 2 x = 2 - 6 x = -4 Therefore: x = -4, y = 6, z = 4

Algebra

Matrices & Determinants

Easy

core

If $\begin{bmatrix} x+y & 4 \\ 1+z & y \end{bmatrix} = \begin{bmatrix} 2 & 4 \\ 5 & 6 \end{bmatrix}$ , then

$x = 4, y = -6, z = 4$

$x = -4, y = 6, z = 4$

$x = -4, y = 6, z = -4$

$x = 4, y = -6, z = -4$

✅ Correct Option: 2

Two matrices are equal when each element in the first matrix equals the corresponding element in the same position in the second matrix.

$\begin{bmatrix} x+y & 4 \\ 1+z & y \end{bmatrix} = \begin{bmatrix} 2 & 4 \\ 5 & 6 \end{bmatrix}$

Comparing corresponding positions:

Top-left: $x + y = 2$ ... (1)

Top-right: $4 = 4$ ✓

Bottom-left: $1 + z = 5$ ... (2)

Bottom-right: $y = 6$ ... (3)

From equation (3):

$y = 6$

From equation (2):

$1 + z = 5$

$z = 5 - 1$

$z = 4$

From equation (1), substituting $y = 6$ :

$x + 6 = 2$

$x = 2 - 6$

$x = -4$

Therefore: $x = -4$ , $y = 6$ , $z = 4$

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Which of the following statements is incorrect?

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If $A = [a_{ij}]_{3\times3}, a_{ij} = 2i-j$ then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
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B.	$\vert A - I \vert$ , I is identity matrix	II.	$-7$
C.	minor of $a_{32}$	III.	$0$
D.	cofactor $a_{32}$	IV.	$-4$

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If $\begin{bmatrix} x+y & 4 \\ 1+z & y \end{bmatrix} = \begin{bmatrix} 2 & 4 \\ 5 & 6 \end{bmatrix}$ , then