If the matrix A = bmatrix & & \\ 0 & 0 & 2 \\ 3 & -2 & 0 bmatrix is a skew symmetric matrix, then the value of ( + + )^2 is: Option 1: 4 Option 2: 16 Option 3: 9 Option 4: 36

Answer: 9. Solution: A matrix is skew-symmetric if it equals the negative of its transpose. This means all diagonal elements must equal zero, and elements at position (i,j) must equal the negative of elements at position (j,i). Given A = bmatrix & & \\ 0 & 0 & 2 \\ 3 & -2 & 0 bmatrix The diagonal elements are, 0, and 0. For a skew-symmetric matrix, all diagonal elements must be zero: = 0 For the element at position (1,2), we have . The mirror element at position (2,1) is 0. For skew-symmetry: = -0 = 0 For the element at position (1,3), we have . The mirror element at position (3,1) is 3. For skew-symmetry: = -3 For the element at position (2,3), we have 2. The mirror element at position (3,2) is -2. Checking: 2 = -(-2) = 2 (satisfied) The values are: = 0 = 0 = -3 Therefore: ( + + )^2 = (0 + 0 + (-3))^2 = (-3)^2 = 9

Algebra

Matrices & Determinants

Medium

applied

If the matrix $A = \begin{bmatrix} \alpha & \beta & \gamma \\ 0 & 0 & 2 \\ 3 & -2 & 0 \end{bmatrix}$ is a skew symmetric matrix, then the value of $(\alpha + \beta + \gamma)^2$ is:

✅ Correct Option: 3

A matrix is skew-symmetric if it equals the negative of its transpose. This means all diagonal elements must equal zero, and elements at position (i,j) must equal the negative of elements at position (j,i).

Given $A = \begin{bmatrix} \alpha & \beta & \gamma \\ 0 & 0 & 2 \\ 3 & -2 & 0 \end{bmatrix}$

The diagonal elements are $\alpha$ , $0$ , and $0$ .

For a skew-symmetric matrix, all diagonal elements must be zero:

$\alpha = 0$

For the element at position (1,2), we have $\beta$ .

The mirror element at position (2,1) is $0$ .

For skew-symmetry: $\beta = -0$

$\beta = 0$

For the element at position (1,3), we have $\gamma$ .

The mirror element at position (3,1) is $3$ .

For skew-symmetry: $\gamma = -3$

For the element at position (2,3), we have $2$ .

The mirror element at position (3,2) is $-2$ .

Checking: $2 = -(-2) = 2$ (satisfied)

The values are:

$\alpha = 0$

$\beta = 0$

$\gamma = -3$

Therefore:

$(\alpha + \beta + \gamma)^2 = (0 + 0 + (-3))^2$

$= (-3)^2$

$= 9$

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Choose the correct answer from the options given below:

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For any matrices A and B of suitable orders,

If the matrix A=[αβγ0023−20]A = \begin{bmatrix} \alpha & \beta & \gamma \\ 0 & 0 & 2 \\ 3 & -2 & 0 \end{bmatrix}A=​α03​β0−2​γ20​​ is a skew symmetric matrix, then the value of (α+β+γ)2(\alpha + \beta + \gamma)^2(α+β+γ)2 is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If the matrix $A = \begin{bmatrix} \alpha & \beta & \gamma \\ 0 & 0 & 2 \\ 3 & -2 & 0 \end{bmatrix}$ is a skew symmetric matrix, then the value of $(\alpha + \beta + \gamma)^2$ is: