Given a vector with cartesian components $(x,y)$, if scaling is done with matrix
$M=\left[\matrix{0.5\quad 0\cr 0\quad 1.5}\right]$
which of the following are true.
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Decreases the vertical by three halves
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Increases the vertical by three halves
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Doubles the horizontal
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Halves the horizontal
Choose the correct answer from the options given below:
π₯ Video solution / Text Solution of this question is given below:
Scaling matrix is:
$M=\left[\matrix{0.5\quad 0\cr 0\quad 1.5}\right]$
Here,
Horizontal scaling factor is:
$S_x=0.5=\frac{1}{2}$
So, horizontal value becomes half.
Therefore, statement $4$ is true.
Vertical scaling factor is:
$S_y=1.5=\frac{3}{2}$
So, vertical value increases by three halves.
Therefore, statement $2$ is true.
Correct statements are:
$2$ and $4$