Given a vector with cartesian components \((x, y)\), if scaling is done with…
2022
Given a vector with cartesian components \((x, y)\), if scaling is done with matrix \(\left[\begin{array}{cc}0.5 & 0 \\ 0 & 1.5\end{array}\right]\), which of the following are true.
A. Decreases the vertical by three halves
B. Increases the vertical by three halves
C. Doubles the horizontal
D. Halves the horizontal
Choose the correct answer from the options given below:
- A.
A and C only
- B.
A and D only
- C.
B and C only
- D.
B and D only
Attempted by 151 students.
Show answer & explanation
Correct answer: D
Key idea: a scaling matrix multiplies each component of the vector by the corresponding diagonal entry.
Horizontal (x) component: multiplied by 0.5 → the horizontal is halved.
Vertical (y) component: multiplied by 1.5 → the vertical is increased by three halves.
Conclusion: The true statements are the ones that say the vertical increases by three halves and the horizontal is halved. The statements claiming the vertical decreases by three halves or that the horizontal doubles are false.