Describe geometrically the effect of the transformation T.
-Let $\mathrm { A } = \left[ \begin{array} { l l } 1 & 0 \ 2 & 1 \end{array} \right]$.
Define a transformation $\mathrm { T }$ by $\mathrm { T } ( \mathrm { x } ) = \mathrm { Ax }$.
A) Vertical shear
B) Projection onto $x _ { 2 }$-axis
C) Projection onto $\mathrm { x } _ { 1 }$-axis
D) Horizontal shear

Question

Quizplus · Accepted Answer

The transformation matrix A shears the space vertically because the off-diagonal element in the first column (2) indicates a vertical distortion, while the diagonal elements (1, 1) preserve the scale along the x and y axes.

Describe Geometrically the Effect of the Transformation T A=[1021]\mathrm { A } = \left[ \begin{array} { l l } 1 & 0 \\ 2 & 1 \end{array} \right]A=[12​01​]

Describe Geometrically the Effect of the Transformation T $\mathrm { A } = \left[ \begin{array} { l l } 1 & 0 \\ 2 & 1 \end{array} \right]$