Tabansi

2020-11-10

Determine if a linear transformation function is

Cullen

Skilled2020-11-11Added 89 answers

Calculation:

The function is defined as,

$T\left(A\right)=\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]A$

Assume two general matrix$A=\left[\begin{array}{ccc}{a}_{11}& {a}_{12}& {a}_{13}\\ {a}_{21}& {a}_{22}& {a}_{23}\\ {a}_{31}& {a}_{32}& {a}_{33}\end{array}\right]{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}B=\left[\begin{array}{ccc}{b}_{11}& {b}_{12}& {b}_{13}\\ {b}_{21}& {b}_{22}& {b}_{23}\\ {b}_{31}& {b}_{32}& {b}_{33}\end{array}\right].$

Then$A+B=\left[\begin{array}{ccc}{a}_{11}+{b}_{11}& {a}_{12}+{b}_{12}& {a}_{13}+{b}_{13}\\ {a}_{21}+{b}_{21}& {a}_{22}+{b}_{22}& {a}_{23}+{b}_{23}\\ {a}_{31}+{b}_{31}& {a}_{32}+{b}_{32}& {a}_{33}+{b}_{33}\end{array}\right]$

$cA=\left[\begin{array}{ccc}c{a}_{11}& c{a}_{12}& c{a}_{13}\\ c{a}_{21}& c{a}_{22}& c{a}_{23}\\ c{a}_{31}& c{a}_{32}& c{a}_{33}\end{array}\right]$

The function ia a linear transformation if it satisfies the the two properties as mentioned in the approach part.

Compute$T(A\text{}+\text{}B)\text{}\text{and}\text{}T(A)\text{}+\text{}T(B)$ as,

The function is defined as,

Assume two general matrix

Then

The function ia a linear transformation if it satisfies the the two properties as mentioned in the approach part.

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