Question

Given the vector (4|3) and the transformation matrix (0|1|-1|0), which vector is the imagine after applying the transformation to (4|3)? A. (4|-3)
B.(-3|4)

C.(3|-4)

D.(-4|3)

Answer 1

Answer:

C.(3|-4)

Step-by-step explanation:

Given the vector:

$\left[\begin{array}{ccc}4\\3\end{array}\right]$

The transformation Matrix is:

$\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]$

The image of the vector after applying the transformation will be:

$\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\left[\begin{array}{ccc}4\\3\end{array}\right]\\\\=\left[\begin{array}{ccc}0*4+1*3\\-1*4+0*3\end{array}\right]\\\\=\left[\begin{array}{ccc}3\\-4\end{array}\right]$

The correct option is C