Determine if a linear transformation function is T:M33, T(A)=[001010100]A

Calculation: The function is defined as, T(A)=[001010100]A Assume two general matrix A=[a11a12a13a21a22a23a31a32a33]andB=[b11b12b13b21b22b23b31b32b33]. Then A+B=[a11+b11a12+b12a13+b13a21+b21a22+b22a23+b23a31+b31a32+b32a33+b33] cA=[ca11ca12ca13ca21ca22ca23ca31ca32ca33] The function ia a linear transformation if it satisfies the the two properties as mentioned in the approach part. Compute T(A + B) and T(A) + T(B) as,

Key to "Determine if a linear transformation function is T:M33,..."

Tabansi

Answered question

2020-11-10

Determine if a linear transformation function is
$T : M_{33},$
$T (A) = [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}] A$

Answer & Explanation

Cullen

Skilled2020-11-11Added 89 answers

Calculation:
The function is defined as,

T (A) = [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}] A

Assume two general matrix

A = [\begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{matrix}] and B = [\begin{matrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \\ b_{31} & b_{32} & b_{33} \end{matrix}] .

Then

A + B = [\begin{matrix} 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{matrix}]

c A = [\begin{matrix} 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{matrix}]

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

T (A + B) and T (A) + T (B)

as,

This is helpful24Flag

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Integral Calculus

Didn't find what you were looking for?