Q5
A Iinear transformation T, defined as \[T [ array*20c x_1 \\ x_2 \\ x_3 array ] = [ array*20c x_1 + x_2 \\ x_2 - x_3 array ],\] transforms a vector \[ x \] for a three-dimensional real space to a two-dimensional real space. The transformation matrix T is
A Iinear transformation T, defined as T\left[ {\begin{array}{*{20}{c}}
{{x_1}} \\
{{x_2}} \\
{{x_3}}
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
{{x_1} + {x_2}} \\
{{x_2} - {x_3}}
\end{array}} \right], transforms a vector for a three-dimensional real space to a two-dimensional real space. The transformation matrix T is
A.
\left[ {\begin{array}{*{20}{c}}
1&1&0 \\
0&1&{ - 1}
\end{array}} \right]
AnswerB.
\left[ {\begin{array}{*{20}{c}}
1&0&0 \\
0&1&0
\end{array}} \right]
C.
\left[ {\begin{array}{*{20}{c}}
1&1&1 \\
{ - 1}&1&1
\end{array}} \right]
D.
\left[ {\begin{array}{*{20}{c}}
1&0&0 \\
0&0&1
\end{array}} \right]
Answer: Option A
Solution
Answer: Option A
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