Describe geometrically the effect of the transformation T.
-Let $A = \left[ \begin{array} { l l l } 0 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$
Define a transformation $\mathrm { T }$ by $\mathrm { T } ( \mathbf { x } ) = \mathrm { Ax }$.
A) Projection onto the $x _ { 2 } \times 3$-plane
B) Projection onto the $x _ { 2 }$-axis
C) Horizontal shear
D) Vertical shear

Question

Quizplus · Accepted Answer

The transformation matrix $A$ has zeros in the first row and ones along the diagonal from the second row onward. This means it projects any vector $\mathbf{x}$ onto the plane defined by the $x_2$ and $x_3$ axes, effectively eliminating the $x_1$ component of the vector.

Describe Geometrically the Effect of the Transformation T A=[000010001]A = \left[ \begin{array} { l l l } 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]A=​000​010​001​​

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