Exercise3

This problem concerns the identification of matrix transformations.

  1. Check that the following function \(T:\real^3\to\real^2\) is a matrix transformation by finding a matrix \(A\) such that \(T(\xvec) = A\xvec\text{.}\)

    \begin{equation*} T\left(\threevec{x_1}{x_2}{x_3}\right) = \left[\begin{array}{c} 3x_1 - x_2 + 4x_3 \\ 5x_2 - x_3 \\ \end{array}\right] \text{.} \end{equation*}
  2. Explain why

    \begin{equation*} T\left(\threevec{x_1}{x_2}{x_3}\right) = \left[\begin{array}{c} 3x_1^4 - x_2 + 4x_3 \\ 5x_2 - x_3 \\ \end{array}\right] \end{equation*}

    is not a matrix transformation.

in-context