The standard ordered basis of ℝ2 is {e1, e2}. Let T : ℝ2 → ℝ2 be the linear transformation such that T reflects the points through the line x1 = -x2. The standard matrix of T is:

Question

The standard ordered basis of ℝ2 is {e1, e2}. Let T : ℝ2 → ℝ2 be the linear transformation such that T reflects the points through the line x1 = -x2. The standard matrix of T is:

TuteeHUB · Accepted Answer

$\left( {\begin{array}{*{20}{c}} -1&0\ 0&-1 \end{array}} \right)$

TuteeHUB · Answer

$\left( {\begin{array}{*{20}{c}} 0&1\ 1&0 \end{array}} \right)$

TuteeHUB · Answer

$\left( {\begin{array}{*{20}{c}} 0&-1\ -1&0 \end{array}} \right)$

TuteeHUB · Answer

$\left( {\begin{array}{*{20}{c}} 1&0\ 0&1 \end{array}} \right)$

1.	The standard ordered basis of ℝ2 is {e1, e2}. Let T : ℝ2 → ℝ2 be the linear transformation such that T reflects the points through the line x1 = -x2. The standard matrix of T is:
A.	\(\left( {\begin{array}{*{20}{c}} 0&1\\ 1&0 \end{array}} \right)\)
B.	\(\left( {\begin{array}{*{20}{c}} 0&-1\\ -1&0 \end{array}} \right)\)
C.	\(\left( {\begin{array}{*{20}{c}} -1&0\\ 0&-1 \end{array}} \right)\)
D.	\(\left( {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right)\)
Answer» C. \(\left( {\begin{array}{*{20}{c}} -1&0\\ 0&-1 \end{array}} \right)\)

The standard ordered basis of ℝ2 is {e1, e2}. Let T : ℝ2 → ℝ2 be the linear transformation such that T reflects the points through the line x1 = -x2. The standard matrix of T is:

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