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Previous Year Question (PYQs)

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.

  1. Decreases the vertical by three halves
  2. Increases the vertical by three halves
  3. Doubles the horizontal
  4. Halves the horizontal

Choose the correct answer from the options given below:





Solution

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 $4$


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