1.9 The Matrix of a Linear Transformation

Question 1

standard matrix for the linear transformation

Answer 1

let T: Rn –> Rm be a linear transformation, T(x)=Ax and A is the standard matrix

Question 2

onto

Answer 2

a mapping T is onto Rm if each b in Rm is the image of AT LEAST ONE x in Rn; linearly dependent (columns of A span Rm)

Question 3

one to one

Answer 3

if each b in Rm is the image of AT MOST ONE x in Rn; linearly independent