Question

This is an assignment so don't give me the answer, only hints. Could someone interpret this question for me?

Write the elements of \(\mathbb{R}^n\) and \(\mathbb{R}^m\) as rows. If \(A\) is an \(m\times n\) matrix, define \(T\colon\mathbb{R}^m\rightarrow \mathbb{R}^n\) by \(T(\mathbf{y})=\mathbf{y}A\) for all rows \(\mathbf{y}\) in \(\mathbb{R}^n\). Show that the rows of \(A\) are \(T(\mathbf{f}_1),\ldots,T(\mathbf{f}_m)\) where \(\mathbf{f}_i\) denotes row \(i\) of \(I_m\).

Answer 1

The domain of \(T\) is \(\mathbb{R}^m\) but \(\mathbf{y}\in\mathbb{R}^n\)?

Answer 2

since http://prntscr.com/455j8w

Answer 3

\(\mathbf{y}\in\mathbb{R}^{\color{red} n}\)

Answer 4

as u can see
T(y) = y A defined on R^n to R^n
then
y in R^n
y A in R^n

Answer 5

\(T\colon\mathbb{R}^{\color{red} m}\rightarrow\mathbb{R}^n\)

Answer 6

well its given :O
if u have T : C^n to R^n

then y in C^n

Answer 7

wait i got u nw
the qn R^m to R^n
nw i got what u mean
so why y in R^m also right ?

Answer 8

well consider this R^m is a group like ?
so its closed , means
if ab=c s.t c in R^m
then a in R^m and b in R^m

Answer 9

its not wrong :D

Answer 10

Is there a typo because \(A_{m\times n}\), \(T\colon\:\mathbb{R}^{\color{red}m}\rightarrow\mathbb{R}^n,\,T(\mathbf{y})=\mathbf{y}A\) yet \(\mathbf{y}\in\mathbb{R}^{\color{red}n}\)?

Answer 11

i dnt think so , maybe its m for a reason

Answer 12

@ikram002p I think we should start at f(i) is row of I_m. f(i) is in R^m
T(I_m)=I_m*A

Answer 13

so no typo ?

Answer 14

But how could you multiply a 1xn matrix with a mxn matrix?

Answer 15

u cant x_X

Answer 16

got what u mean , a bit confused sry :|
for definition of grouping no problem
but solving with matrix ,,, mm