Question

The transformation 'orthogonal projection on X- axis' is given by matrix

• A. $\begin{bmatrix}0&1\\\ 0&0\end{bmatrix}$
• B. $\begin{bmatrix}0& 0 \\\ 1 &0\end{bmatrix}$
• C. $\begin{bmatrix} 1 &0 \\\ 0&0\end{bmatrix}$
• D. $\begin{bmatrix}0& 0 \\\ 0 & 1\end{bmatrix}$

Answer 1

Answer: (C)

$\begin{bmatrix} 1 &0 \\\ 0&0\end{bmatrix}$

Answer 2

Under the given transformation, a point (x, y) is transformed to (x, 0), i.e., the foot of perpendicular from (x, y) on the x-axis. Now $x = 1x + 0y$ and $0 = 0x + 0y$, therefore, the required matrix of the transformation is $\begin{bmatrix} 1 & 0 \\\ 0&0\end{bmatrix}$