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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If the sum of the matrices $\begin{bmatrix}\text{x}\\\text{x}\\\text{y}\end{bmatrix},\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}$ and $\begin{bmatrix}\text{z}\\0\\0\end{bmatrix}$ is the matrix $\begin{bmatrix}10\\5\\5\end{bmatrix},$ then what is the value of $y ?$
  • A
    $-5$
  • ✓
    $0$
  • C
    $5$
  • D
    $10$
✓

Answer

Correct option: B.
$0$
$\begin{bmatrix}\text{x}\\\text{x}\\\text{y}\end{bmatrix}+\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}+\begin{bmatrix}\text{z}\\0\\0\end{bmatrix}=\begin{bmatrix}10\\5\\5\end{bmatrix}$
$\therefore\text{x}+\text{y}+\text{z}=10,\text{ x}+\text{y}=5$
$\text{y}+\text{z}=5$ Replacing $\text{x}+\text{y}=5$ in $\text{x}+\text{y}=\text{z}=10$
We have, $\text{z}=5$
Also, $\text{y}+\text{z}=5$
$\therefore\text{y}=5-\text{z}=0$​​​​

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