Activity2.6.2

MATRIX-MULT-2

For the following matrices \(A\) given below, use the diagram to study the effect of the corresponding matrix transformation \(T(\xvec) = A\xvec\text{.}\) For each transformation, describe the geometric effect of the transformation on the plane.

  1. The matrix \(A=\left[\begin{array}{rr} 2 \amp 0 \\ 0 \amp 1 \\ \end{array}\right]\text{.}\)

  2. The matrix \(A=\left[\begin{array}{rr} 2 \amp 0 \\ 0 \amp 2 \\ \end{array}\right]\text{.}\)

  3. The matrix \(A=\left[\begin{array}{rr} 0 \amp -1 \\ 1 \amp 0 \\ \end{array}\right]\text{.}\)

  4. The matrix \(A=\left[\begin{array}{rr} 1 \amp 1 \\ 0 \amp 1 \\ \end{array}\right]\text{.}\)

  5. The matrix \(A=\left[\begin{array}{rr} -1 \amp 0 \\ 0 \amp 1 \\ \end{array}\right]\text{.}\)

  6. The matrix \(A=\left[\begin{array}{rr} 1 \amp 0 \\ 0 \amp 0 \\ \end{array}\right]\text{.}\)

  7. The matrix \(A=\left[\begin{array}{rr} 1 \amp 0 \\ 0 \amp 1 \\ \end{array}\right]\text{.}\)

  8. The matrix \(A=\left[\begin{array}{rr} 1 \amp -1 \\ -2 \amp 2 \\ \end{array}\right]\text{.}\)

in-context