Question: Let L: Rn Rm be a linear transformation defined by L(x) = Ax, for x in R. Prove that L is onto if and only

Let L: Rn Rm be a linear transformation defined by L(x) = Ax, for x in R". Prove that L is onto if and only if rank A = m.

Step by Step Solution

3.37 Rating (175 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let L R n R m is defined by Lx Ax where A is m n suppose that L is onto ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

951-M-L-A-L-S (7081).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!