Question

Consider the linear transformation T: R3 + R2 defined as T(X1, X2, 23)=(-23, -3 &1 – 23).

Answer 1

$T : R^3\rightarrow R^2$

as we are defining composition H must be from $H : R^2 \rightarrow R^2$

$H_oT(x)=H(T(x))$   

x = (01 1,C2, 13 ER

$H_oT : R^3 \rightarrow R^2$

so the standard matrix must be 2 X 3 matrix

H is a reflection from

(01) Reflection through th g-aris (-10) (10) e,= (10) (۰) رم Hle) = (-10) Hle) = 10 ) Find formula for H x ] (07 y [o] apply H H fit an[:M19 [:]+4 [o] [x 20 here (ay) EiR3 don't get confused with both sc

therefore

$H\begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} -x\\ y \end{bmatrix}$

  

so standard matrix for $H_oT$

$\\*H_oT(x)= Ax \\*H_oT(x)=\begin{bmatrix} 0 &0 &1 \\ -3&0 &-1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}$

$A = \begin{bmatrix} 0 & 0 & 1\\ -3& 0 &-1 \end{bmatrix}$ standard matrix .