Question

determine whether the following are linear transformation.
a)T:Mnn->R,where T(A)=tr(A)
b)T:Mmn->R, where T(A)=transpose of A

Answer 1

hlp pls

Answer 2

@amistre64

Answer 3

yes they are: let \(A=(a_{ij})\) and \(B=(b_{ij})\)
(i)
\[ \large \text{tr}(A+B)=\sum_{i=1}^n(A+B)_{ii}=\sum_{i= 1}^n(a_{ii}+b_{ii})\]
\[ \large =\sum_{i=1}^na_{ii}+\sum_{i=1}^nb_{ii}=\text{tr}(A)+\text{tr}(B). \]
and
\[ \large \text{tr}(\alpha A)=\sum_{i=1}^n(\alpha A)_{ii}=\sum_{i=1}^n(\alpha a_{ii})
=\alpha\sum_{i=1}^na_{ii}=\alpha\cdot\text{tr}(A) \]

Answer 4

quite the same for (ii)

Answer 5

is it not suppose to be in the formof matrices

Answer 6

@TuringTest ,hlp pls

Answer 7

the 2nd one plz