Mention the type of matrix {bmatrix} 0 & -3 & -2 \\ 3 & 0 & -1 \\ 2 & 1 & 0 {bmatrix}

Correct Answer is : square matrix

Correct Answer is : square matrix

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Question : 6 of 36

Marks: +1, -0

\begin{bmatrix} 0 & -3 & -2 \\ 3 & 0 & -1 \\ 2 & 1 & 0 \end{bmatrix}

Solution:

Concept:

A skew-symmetric matrix satisfies

A^T = -A

, meaning its transpose equals its negative.

Explanation:

Let

A = \begin{bmatrix} 0 & -3 & -2 \\ 3 & 0 & -1 \\ 2 & 1 & 0 \end{bmatrix}

Compute

A^T

: rows become columns →

A^T = \begin{bmatrix} 0 & 3 & 2 \\ -3 & 0 & 1 \\ -2 & -1 & 0 \end{bmatrix}

Compute

-A = \begin{bmatrix} 0 & 3 & 2 \\ -3 & 0 & 1 \\ -2 & -1 & 0 \end{bmatrix}

Since

A^T = -A

, the matrix is skew-symmetric.

Also note that all diagonal entries are zero, confirming the property.

Answer:

The matrix is a skew symmetric matrix.

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