If \(3\begin{bmatrix}x&y\\z&w\end{bmatrix} = \begin{bmatrix}x&6\\-1&2w\end{bmatrix} +\begin{bmatrix}4&x+y\\z+w&3\end{bmatrix}\), then the values of \(x, y, z\) and \(w\) are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(x = 2, y = 4, z = 1, w = 3\)
Adding the matrices on the right:
\( \displaystyle \begin{bmatrix}3x&3y\\3z&3w\end{bmatrix} = \begin{bmatrix}x + 4&6 + x + y\\-1 + z + w&2w + 3\end{bmatrix} \)
Equal matrices have equal corresponding entries:
\(3x = x + 4,\quad x = 2\)
\(3w = 2w + 3,\quad w = 3\)
\(3y = 6 + 2 + y,\quad y = 4\)
\(3z = -1 + z + 3,\quad z = 1\)
NCERT (2026-27 edition):
Operations on Matrices
