To sketch: (i) The properties, (ii) Linear transformation. Let {T}:mathbb{R}^{2}tomathbb{R}^{2} be the linear transformation that reflects each point through the x_{1} axis. Let {A}={left[begin{matrix}{1}&{0}{0}&-{1}end{matrix}right]}

preprekomW 2021-02-03 Answered
To sketch:
(i) The properties,
(ii) Linear transformation.
Let T:R2R2 be the linear transformation that reflects each point through the
x1axis.
Let A=[1001]
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Expert Answer

wheezym
Answered 2021-02-04 Author has 103 answers

Assume the value of u=[24],v=[63].
Consider some random points for u and v.
The value of u + v.
u+v=[24]+[63]
=[87]
The transformation xAx reflects points through the x1 -axis.
Determine the value of T(u):
T(u)=Au
=[1001][24]
=[24]
Determine the value of T(v):
T(v)=Av
=[1001][63]
=[63]
Determine the value of T(u + v):
T(u + v)=A(u + v)
=[1001][87]
=[87]
Show the values of the vectors as in Figure 1.
image
Linear transformation:
Consider the value of c as 2.
Thus the value of cu is:
cu=2×[24]=[48]
Determine the transformation of cu.
T(cu)=[1001][48]
=[48]
Show the linear transformation of T as in Figure 2.
image

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