midterm1 Practice Solutions

# midterm1 Practice Solutions - Math 136 Additional Practice...

This preview shows pages 1–2. Sign up to view the full content.

Math 136 Additional Practice for Term Test 1 Solutions 1: Let B = 1 1 2 , 1 1 3 , 5 1 0 . (a) Determine if vectorv = 0 5 5 is in span B . Solution: We need to determine if there exists c 1 ,c 2 ,c 3 such that 0 5 5 = c 1 1 1 2 + c 2 1 1 3 + c 3 5 1 0 = c 1 + c 2 + 5 c 3 c 1 c 2 + c 3 2 c 1 + 3 c 2 Comparing entries, we see that we need to determine whether the system c 1 + c 2 + 5 c 3 = 0 c 1 c 2 + c 3 = 5 2 c 1 + 3 c 2 = 5 is consistent or not. Row reducing the corresponding augmented matrix to RREF gives 1 1 5 0 1 1 1 5 2 3 0 5 1 0 3 0 0 1 2 0 0 0 0 1 Therefore, the rank of the coefficient matrix is less than the rank of the augmented matrix, thus the system is inconsistent. Therefore, vectorv is not in the span of B . (b) Determine if B is linearly independent or linearly dependent. Solution: Consider 0 0 5 = c 1 1 1 2 + c 2 1 1 3 + c 3 5 1 0 = c 1 + c 2 + 5 c 3 c 1 c 2 + c 3 2 c 1 + 3 c 2 We see that we get a homogeneous system with the same coefficient matrix as in (a).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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