Answer to Question #159965 in Linear Algebra for UMAR

Question

Let T and U be the linear operator on R^2 defined by

T(x1,x2)=(x2,x1) and U(x1,X2)=(x1,0)

A) How would you describe T and U in geometrically

B) give rules like the ones defining..

Answer 1

Both functions T and U are linear transformations thus having linear components. T has (x2,x1) and U has (x1,0) which satisfy the rule of linear transformation A linear transformation is a function T:R^n

→R^m

T:R^n→R^m that satisfies the following properties:

1. T(x+y)=T(x)
2. T(ax)=aT(x)

for any vectors x,y∈R

n

x,y∈Rn and any scalar a∈R