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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES1 Mark
MCQ
The matrix $\begin{bmatrix}0&\text{amp; }1\\1&\text{amp; }0\end{bmatrix}$ is the matrix reflection in the line:
  • A
    x = 1
  • B
    x + y = 1
  • C
    y = 1
  • ✓
    x = y
✓

Answer

Correct option: D.
x = y
We know that the reflection matrix through a line $\text{y}=\text{mx}$ making an $\angle \theta$ with x - axis is given as.
$\begin{bmatrix} \cos { 2\theta }&\text{amp;}\sin { 2\theta } \\ \sin { 2\theta } &\text{amp;} -\cos { 2\theta }\end{bmatrix}$

Given transformation matrix is $\begin{bmatrix}0&\text{amp; }1\\1&\text{amp; }0\end{bmatrix}$

$\Rightarrow\cos2\theta=0\sin2\theta=1$

$\Rightarrow 2\theta ={90}^{0}$

$\Rightarrow \theta={45}^{0}$

$\Rightarrow \tan \theta=1$

Hence, the line of reflection is $\text{y}=\text{x}$

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