Question

41. On a separate sheet of paper, transform the vector [1 0 sh What is the y-value of the terminal point of the resulting vector? y = AN

Answer 1

The given matrix is

$\small A=\begin{pmatrix} 0 & 1\\ 1& 0 \end{pmatrix}$

And the vector shown has it's tail three units to the left of the origin and 1 unit upwards, so the vector is given by

$\small \begin{pmatrix} -3\\ 1 \end{pmatrix}$

Then, the transformed vector is obtained by multiplying the given matrix with the given vector as

$\small \begin{pmatrix} 0 & 1\\ 1 & 0 \end{pmatrix}\begin{pmatrix} -3\\ 1 \end{pmatrix}=\begin{pmatrix} 1\\ -3 \end{pmatrix}$

Which is the vector given by:

-6 -4 -2 0 2 4 6

Thus, the y-value of the terminal point of the resulting vector is -3