Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 302: 81

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Be A and B, arrays of $M_{nn}$ and $c$ is a scalar number, then: 1. $ T (A+B)=T(A)+T(B)$ $ T (A+B)= (a_{11}+...+a_{nn}+b_{11}+...+b_{nn})$ $ T (A)+T(B)= (a_{11}+...+a_{nn})+(b_{11}+...+b_{nn})$ $ T (A)+T(B)= (a_{11}+...+a_{nn}+b_{11}+...+b_{nn})$ $ T (A+B)=T(A)+T(B)$ 2. $T(ca)=cT(A)$ $T(cA)= (c a_{11} +...+c a_{nn})$ $T(cA)= c (a_{11} +...+a_{nn})$ $cT(A)$= $c (a_{11} +...+a_{nn})$ $T(cA)=cT(A)$