Linear algebra problem?
Let the set { e1,e2,e3} be the standard basis of R^3(R).The linear transformation T:R^3(R) -->R^3(R) is defined as T(e1)=e1+e2 , T(e2)=e1-e2+e3, T(e3)=3e1+4e3.Show that T is a non singular and find the inverse of T.
Let the set { e1,e2,e3} be the standard basis of R^3(R).The linear transformation T:R^3(R) -->R^3(R) is defined as T(e1)=e1+e2 , T(e2)=e1-e2+e3, T(e3)=3e1+4e3.Show that T is a non singular and find the inverse of T.
Comments
We can write the matrix corresponding to transformation T as
A =
[1....1....3]
[1...-1....0]
[0....1....4]
It's up to you to show that this matrix is non-singular and find its inverse.
Hope that helps!