{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Math_307_Section_102_December_2006

# Math_307_Section_102_December_2006 - Math 307 Section 102 8...

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

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.

Unformatted text preview: Math 307, Section 102 8 Problems for a total of 85 points Final Exam Friday, December 15, 2006. No books, notes or calculators Problem 1. (10 points) (The scalar field is R .) Consider the matrix A and column vector ~ b : A = 1 1 1 0 0 1 2 3 4 ~ b = 1 2 3 (a) (6 points) Find the PA = LU factorization for A . (b) (2 points) Recall that the PA = LU factorization can be used to rewrite the system A~x = ~ b as two systems with triangular coefficient matrix. Write down these two triangular systems. (c) (2 points) Solve the two triangular systems to find all ~x such that A~x = ~ b . Problem 2. (10 points) (The scalar field is R .) Consider the matrix A = 1 2 3 4 2 4 3 0 5 1 2- 1 5 5 (a) Find a basis for the nullspace of A . (b) Find a basis for the column space of A . (c) Find a basis for the left nullspace of A . (d) Find a basis for the row space of A ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

Math_307_Section_102_December_2006 - Math 307 Section 102 8...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online