91Ó°ÊÓ

In Problems \(43-46\), find the parametric equation of the line in the \(x-y\) plane that goes through the indicated point in the direction of the indicated vector. $$ (1,-1),\left[\begin{array}{l} 2 \\ 1 \end{array}\right] $$

Use a rotation matrix to rotate the vector \begin{tabular}{|l|l} 5 & counterclock- \\ 2 \end{tabular} wise by the angle \(\pi / 12\).

Show that the inverse of $$ A=\left[\begin{array}{ll} 2 & 1 \\ 1 & 1 \end{array}\right] $$ is $$ B=\left[\begin{array}{rr} 1 & -1 \\ -1 & 2 \end{array}\right] $$

Find the parametric equation of the line in the \(x-y\) plane that goes through the indicated point in the direction of the indicated vector. $$ (3,-4),\left[\begin{array}{r} -1 \\ 2 \end{array}\right] $$

Show that the inverse of $$ A=\left[\begin{array}{lll} 2 & 3 & 1 \\ 5 & 2 & 3 \\ 1 & 2 & 0 \end{array}\right] $$ is $$ B=\left[\begin{array}{rrr} -\frac{6}{5} & \frac{2}{5} & \frac{7}{5} \\ \frac{3}{5} & -\frac{1}{5} & -\frac{1}{5} \\ \frac{8}{5} & -\frac{1}{5} & -\frac{11}{5} \end{array}\right] $$

Use a rotation matrix to rotate the vector \(\left[\begin{array}{l}-2 \\\ -3\end{array}\right]\) counterclockwise by the angle \(\pi / 9\).

$$ A=\left[\begin{array}{rr} -1 & 1 \\ 2 & 3 \end{array}\right], \quad B=\left[\begin{array}{rr} 2 & -2 \\ 3 & 2 \end{array}\right] $$ Find the inverse (if it exists) of \(A\).

Find the parametric equation of the line in the \(x-y\) plane that goes through the indicated point in the direction of the indicated vector. $$ (-1,-2),\left[\begin{array}{r} 1 \\ -3 \end{array}\right] $$

Find the parametric equation of the line in the \(x-y\) plane that goes through the indicated point in the direction of the indicated vector. $$ (-1,4),\left[\begin{array}{l} 2 \\ 3 \end{array}\right] $$

$$ A=\left[\begin{array}{rr} -1 & 1 \\ 2 & 3 \end{array}\right], \quad B=\left[\begin{array}{rr} 2 & -2 \\ 3 & 2 \end{array}\right] $$ Find the inverse (if it exists) of \(B\).