If \(\begin{bmatrix}1&2&1\end{bmatrix}\begin{bmatrix}1&2&0\\2&0&1\\1&0&2\end{bmatrix}\begin{bmatrix}0\\2\\x\end{bmatrix} = 0\), then value of \(x\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → −1
Multiplying the last two matrices first (row by column):
\( \begin{bmatrix}1&2&0\\2&0&1\\1&0&2\end{bmatrix}\begin{bmatrix}0\\2\\x\end{bmatrix} = \begin{bmatrix}0 + 4 + 0\\0 + 0 + x\\0 + 0 + 2x\end{bmatrix} = \begin{bmatrix}4\\x\\2x\end{bmatrix} \)
Then
\( \begin{bmatrix}1&2&1\end{bmatrix}\begin{bmatrix}4\\x\\2x\end{bmatrix} = \begin{bmatrix}4 + 2x + 2x\end{bmatrix} = \begin{bmatrix}4 + 4x\end{bmatrix} \)
The product is a 1 × 1 matrix, and it equals 0:
\(4 + 4x = 0\)
\(x = -1\)
NCERT (2026-27 edition):
Matrices
