Algebra

Matrices & Determinants

Medium

applied

If $\begin{bmatrix} x-y & t \\ 2x-y & w \end{bmatrix} = \begin{bmatrix} -1 & 2 \\ 0 & 1 \end{bmatrix}$ , then $2x + y + 3t + w$ is equal to

✅ Correct Option: 2

The given matrices are equal:

$\begin{bmatrix} x-y & t \\ 2x-y & w \end{bmatrix} = \begin{bmatrix} -1 & 2 \\ 0 & 1 \end{bmatrix}$

When two matrices are equal, each corresponding element is equal.

From the corresponding elements:

$x - y = -1$ ... (1)

$t = 2$ ... (2)

$2x - y = 0$ ... (3)

$w = 1$ ... (4)

Subtracting equation (1) from equation (3):

$(2x - y) - (x - y) = 0 - (-1)$

$2x - y - x + y = 1$

$x = 1$

Substituting $x = 1$ into equation (1):

$1 - y = -1$

$-y = -2$

$y = 2$

The values are:

$x = 1$

$y = 2$

$t = 2$

$w = 1$

Therefore:

$2x + y + 3t + w$

$= 2(1) + 2 + 3(2) + 1$

$= 2 + 2 + 6 + 1$

$= 11$

2022: 17 Aug Shift 2

Match List - I with List - II.

List - I	List - II
(A) $A$ is a square matrix of order $3$ and $\lvert 2A \rvert = k\lvert A \rvert$ , then $k$ is	(I) $0$
(B) Value of $\begin{vmatrix}1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b\end{vmatrix}$ is	(II) $3$
(C) Matrix $\begin{bmatrix}5-x & x+1 \\ 2 & 4\end{bmatrix}$ is singular, then $x =$	(III) $8$
(D) If $A = (a_{ij}) = \begin{bmatrix}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{bmatrix}$ , then the minor of the element $a_{23}$ is	(IV) $7$

Choose the correct answer from the options given below :

2026: 19 May Shift 1

Which of the following are TRUE?

(A) The inverse of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\frac{1}{27}\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$ .

(B) The determinant of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is 29.

(C) The inverse of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\frac{1}{29}\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$ .

(D) The adjoint of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$ .

Choose the correct answer from the options given below:

2026: 29 May Shift 1

Let $A=\begin{bmatrix}a & 0 \\ b & 0\end{bmatrix}$ and $A^2=\begin{bmatrix}4 & c \\ 2 & 0\end{bmatrix}$ , $a,b,c \in \mathbb{Z}$ . Then the minimum value of $a+b+c$ is:

2025: 13 May Shift 2

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ then $A^{-1}$ is equal to

2026: 26 May Shift 2

The value/s of ' $\lambda$ ' for which the system of equations

$\lambda x + 3y - z = 1$

$x + 2y + z = 2$

$-\lambda x + y + 2z = -1$

has unique solution is/are:

(where $R$ is set of real numbers)

2025: 21 May Shift 1

If $\begin{bmatrix} 1 & 3 & 9 \\ 1 & x & x^2 \\ 4 & 6 & 9 \end{bmatrix}$ is singular matrix, where $x \in \mathbb{N}$ (where N set of natural number), then x is equal to

If [x−yt2x−yw]=[−1201]\begin{bmatrix} x-y & t \\ 2x-y & w \end{bmatrix} = \begin{bmatrix} -1 & 2 \\ 0 & 1 \end{bmatrix}[x−y2x−y​tw​]=[−10​21​], then 2x+y+3t+w2x + y + 3t + w2x+y+3t+w is equal to

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

If $\begin{bmatrix} x-y & t \\ 2x-y & w \end{bmatrix} = \begin{bmatrix} -1 & 2 \\ 0 & 1 \end{bmatrix}$ , then $2x + y + 3t + w$ is equal to