Question

Check if T:IR³—> IR³ given by T([x, y, z]) = [2x, x + y + z, - y] is an isomorphism or not

Answer 1

Answer:

Recall the definition of a linear transformation. Let V and W be two subspaces of Rn and Rm respectively. A mapping T:V→W is called a linear transformation or linear map if it preserves the algebraic operations of addition and scalar multiplication. Specifically, if a,b are scalars and →x,→y are vectors,

T(a→x+b→y)=aT(→x)+bT(→y)

Consider the following important definition.