Question

Let T: R3 →R2 be a Linear transformation such that T (2e1 – e2 + 5e3 ) =[3 -1] T( -e1+e2+5e3) = [ 2 -3] T( e1 – e2 + e3) = [ 2 1] Find the matrix A of transformation such that T(x) = A x

Answer 1

this is not ringing any bells with me.

Answer 2

i would add
T (2e1 – e2 + 5e3 ) =[3 -1]
with
T( -e1+e2+5e3) = [ 2 -3]

to get T(e1)

now you know the first column of the matrix.

same way you can get T(e3)
and then using them get T(e2)

then youll have all three columns of the matrix.

Answer 3

(it will be a matrix of 2X3)

Answer 4

find out T(e1) , T(e2) , T(e3)

each of them is a column in the matrix.
e1 - column 1
etc

Answer 5

A would be 2X3 matrix

Answer 6

i said :
"i would add
T (2e1 – e2 + 5e3 ) =[3 -1]
with
T( -e1+e2+5e3) = [ 2 -3]

to get T(e1)"

lets do it

T(e1) = [5 -4]

so :