Question

3) Find the standard matrix of a linear transformation, or state that the transformation is non-linear and explain what makes it non-linear. a) $T(x) = \begin{pmatrix} x_2 - 1 \ x_1 \ x_3 \end{pmatrix}$ b) $T(x) = \begin{pmatrix} x_1 + x_2 - x_3 \ x_2^2 + 3x_3 \ 2x_1 - 5x_2 \end{pmatrix}$ c) $T(x) = \begin{pmatrix} x_1 + x_2 \ 0 \ x_2 + x_3 \end{pmatrix}$ d) Find the standard matrix of a linear transformation that first rotates every vector by 90° clockwise, and then reflects it about the horizontal axis.

          3) Find the standard matrix of a linear transformation, or state that the transformation is non-linear
and explain what makes it non-linear.
a) $T(x) = \begin{pmatrix} x_2 - 1 \ x_1 \ x_3 \end{pmatrix}$
b) $T(x) = \begin{pmatrix} x_1 + x_2 - x_3 \ x_2^2 + 3x_3 \ 2x_1 - 5x_2 \end{pmatrix}$
c) $T(x) = \begin{pmatrix} x_1 + x_2 \ 0 \ x_2 + x_3 \end{pmatrix}$
d) Find the standard matrix of a linear transformation that first rotates every vector by 90° clockwise,
and then reflects it about the horizontal axis.

3) Find the standard matrix of a linear transformation, or state that the transformation is non-linear
and explain what makes it non-linear.
a) T(x) =
< p m a t r i x >
b) T(x) =
< p m a t r i x >
c) T(x) =
< p m a t r i x >
d) Find the standard matrix of a linear transformation that first rotates every vector by 90° clockwise,
and then reflects it about the horizontal axis.

Added by Kimberly B.

Question

Please give Ace some feedback