b With x x 1 x 2 x 3 this is the same as Ax bfor some x R 3 To see whether the

# B with x x 1 x 2 x 3 this is the same as ax bfor some

• 2

This preview shows page 2 out of 2 pages.

b With ~x = x 1 x 2 x 3 , this is the same as A~x = ~ b for some ~x R 3 . To see whether the linear system A~x = ~ b has a solution we row-reduce the augmented matrix 1 0 5 2 - 2 1 - 6 - 1 0 2 8 6 7→ 1 0 5 2 0 1 4 3 0 0 0 0 The equivalent system has (infinitely many) solutions, x 1 = 2 - 5 x 3 , x 2 = 3 - 4 x 3 , x 3 R is free For example x 1 = 2, x 2 = 3, x 3 = 0 is one such solution, and it is easy to check that it indeed gives the right answer: 2 1 - 2 0 + 3 0 1 2 + 0 5 - 6 8 = 2 - 1 6 (1) So ~ b is indeed in the span of the columns of A , and one such linear combination of the columns is written in equation (1). Answer: ~ b is in the span of the columns of A 2. Matrix A = 1 2 3 4 5 2 2 4 6 1 3 2 5 8 2 4 - 3 1 5 3 is row equivalent to matrix B = 1 0 1 2 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 . Use this fact to describe all solutions of equation A~x = ~ 0 in parametric vector form (or as a span). Answer: This problems is similar to problems 8, 11 in Section 1.5. Equation A~x = 0 w has the same solution set as equation B~x = 0, and matrix B is in reduced echelon form. The free variables are x 3 , x 4 and the basic variables

#### You've reached the end of your free preview.

Want to read both pages?

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
Ask Expert Tutors