Algebra

Matrices & Determinants

Medium

common

If $\begin{bmatrix} 1 & 0 & 0 \\ 0 & y+1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 2x & \\ -2 & \\ z-3 & \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 1 \end{bmatrix}$ then $x + y + z$ is

✅ Correct Option: 2

The first matrix is a diagonal matrix, which simplifies the multiplication.

When multiplying the matrices, each row of the first matrix multiplies with the column of the second matrix.

First row calculation:

$(1)(2x) + (0)(-2) + (0)(z-3)$

$= 2x$

Second row calculation:

$(0)(2x) + (y+1)(-2) + (0)(z-3)$

$= -2(y+1)$

$= -2y - 2$

Third row calculation:

$(0)(2x) + (0)(-2) + (1)(z-3)$

$= z - 3$

After multiplication:

$\begin{bmatrix} 2x \\ -2y-2 \\ z-3 \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 1 \end{bmatrix}$

This gives three equations:

$2x = 6$

$-2y - 2 = 4$

$z - 3 = 1$

For $x$ :

$2x = 6$

$x = 3$

For $y$ :

$-2y - 2 = 4$

$-2y = 6$

$y = -3$

For $z$ :

$z - 3 = 1$

$z = 4$

Therefore:

$x + y + z$

$= 3 + (-3) + 4$

$= 4$

2025: 30 May Shift 2

Which of the following statement('s) is/are TRUE?

(A) Skew symmetric matrix of even order is always symmetric

(B) Skew symmetric matrix of odd order is non-singular

(D) Skew symmetric matrix is always square matrix

Choose the correct answer from the options given below:

2026: 15 May Shift 1

For $\Delta = \begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$ where $a, b, c$ are roots of equation $x^3 + px + q = 0$ , then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$a + b + c$	I.	$p - q$
B.	$\Delta$	II.	$-q$
C.	$ab + bc + ca$	III.	$0$
D.	$abc$	IV.	$p$

Choose the correct answer from the options given below:

2026: 21 May Shift 1

For any 3 ×3 matrix $A$ , if $A(adj\,A) = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}$ , then $2|A|$ is equal to

2023: 15 June Shift 2

If the points (2, 1), $(-1, 4)$ and (a, 3) are collinear then the value/(s) of a is/(are) :

2026: 26 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Column matrix	I.	$\begin{bmatrix}1 & 2 & 3\end{bmatrix}$
B.	Row matrix	II.	$\begin{bmatrix}1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\end{bmatrix}$
C.	Diagonal matrix	III.	$\begin{bmatrix}1\\ 2\\ 3\end{bmatrix}$
D.	Scalar matrix	IV.	$\begin{bmatrix}2 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2\end{bmatrix}$

Choose the correct answer from the options given below:

2025: 13 May Shift 1

If A and B are invertible matrices of same order, then which one of the following is NOT true?

If [1000y+10001][2x−2z−3]=[641]\begin{bmatrix} 1 & 0 & 0 \\ 0 & y+1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 2x & \\ -2 & \\ z-3 & \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 1 \end{bmatrix}​100​0y+10​001​​​2x−2z−3​​​=​641​​ then x+y+zx + y + zx+y+z is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $\begin{bmatrix} 1 & 0 & 0 \\ 0 & y+1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 2x & \\ -2 & \\ z-3 & \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 1 \end{bmatrix}$ then $x + y + z$ is