Morning,

Question

Bit confused:

I have been given the following:

g(x,y)=(4x,6y)
h(x,y)=(x+2y,y)
k(x,y)=(y,x)

and ive got the following matrix for each of them:

g={{4,0},{0,6}}
h={{1,2},{0,1}}
k={{0,1},{1,0}}

So ive been asked to prove the linear transformation f=k.h.g
has the matrix:

A={{0,6},{4,12}}

but with my matrix work ive done above I get the 6 and the 4 the other way around. Any idea where I went wrong?

Thanks

Answer 1

To add this is the matrix multiplication im doing to get the answer:
{{4,0},{0,6}}*{{0,1},{1,0}}*{{1,2},{0,1}

Answer 2

first h*g
4 12
0 6

then k * h*g
0 6
4 12

in detail
h * g
|1 2| | 4 0 | |4 12|
|0 1| | 0 6 | |0 6 |
then
|0 1| |4 12| |0 6 |
|1 0| |0 6 | |4 12|