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Physics Question on Mathematical Methods

Inverse of the matrix [110 230 101]\begin{bmatrix} 1 & 1 & 0 \\\ 2 & 3 & 0 \\\ 1 & 0 & 1 \end{bmatrix} is

A

[1−21 −130 001]\begin{bmatrix} 1 & -2 & 1 \\\ -1 & 3 & 0 \\\ 0 & 0 & 1 \end{bmatrix}

B

[3−10 −210 −311]\begin{bmatrix} 3 & -1 & 0 \\\ -2 & 1 & 0 \\\ -3 & 1 & 1 \end{bmatrix}

C

[−1−10 230 101]\begin{bmatrix} -1 & -1 & 0 \\\ 2 & 3 & 0 \\\ 1 & 0 & 1 \end{bmatrix}

D

[3−2−3 −211 001]\begin{bmatrix} 3 & -2 & -3 \\\ -2 & 1 & 1 \\\ 0 & 0 & 1 \end{bmatrix}

Answer

[3−10 −210 −311]\begin{bmatrix} 3 & -1 & 0 \\\ -2 & 1 & 0 \\\ -3 & 1 & 1 \end{bmatrix}

Explanation

Solution

The correct option is (B) : [3−10 −210 −311]\begin{bmatrix} 3 & -1 & 0 \\\ -2 & 1 & 0 \\\ -3 & 1 & 1 \end{bmatrix}.