Solution Found!

Removing zero rows of U leaves A = LU, where the r columns or L span the column space of

Chapter 6, Problem 6.3.21

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Removing zero rows of U leaves A = LU, where the r columns or L span the column space of A and the r rows of U span the row space. Then A + has the explicit formula U T (U U T ) 1 (L TL) 1L T . Why is A +b in the row space with U T at the front? Why does A TAA+b = A Tb, so that x + = A +b satisfies the normal equation as it should?

Questions & Answers

QUESTION:

Removing zero rows of U leaves A = LU, where the r columns or L span the column space of A and the r rows of U span the row space. Then A + has the explicit formula U T (U U T ) 1 (L TL) 1L T . Why is A +b in the row space with U T at the front? Why does A TAA+b = A Tb, so that x + = A +b satisfies the normal equation as it should?

ANSWER:

Step 1 of 5

Given that  and the rows of  span the row space of . So, the column of  span the row space of .

Consider, the columns of  by  and the given explicit formula for  is

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back