If \(\begin{bmatrix}1&0&0\\0&y+1&0\\0&0&1\end{bmatrix}\begin{bmatrix}2x\\-2\\z-3\end{bmatrix}=\begin{bmatrix}6\\4\\1\end{bmatrix}\) then \(x+y+z\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
Multiplying the matrices (each row of the first matrix has only one non-zero entry):
\( \begin{bmatrix}2x\\-2(y+1)\\z-3\end{bmatrix}=\begin{bmatrix}6\\4\\1\end{bmatrix} \)
Equal matrices have equal corresponding entries:
\(2x = 6,\quad x = 3\)
\(-2(y + 1) = 4,\quad y + 1 = -2,\quad y = -3\)
\(z - 3 = 1,\quad z = 4\)
So
\(x + y + z = 3 - 3 + 4 = 4\)