{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2009bfinweb

# 2009bfinweb - M346 Final Exam 1325 1 0 0 4/11 2 1 1 1 0 1 0...

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

M346 Final Exam, December 15, 2009 1) The matrix A = 1 3 2 5 2 1 1 1 0 1 2 3 3 3 5 7 row-reduces to B = 1 0 0 4 / 11 0 1 0 13 / 11 0 0 1 10 / 11 0 0 0 0 . a)Find all solutions to A x = 0. b)Find a basis for the column space of A . c)In R 3 [ t ], let V be the span of the vectors { 1 + 2 t + 3 t 3 , 3 t + t 2 + 3 t 3 , 2 + t + 2 t 2 + 5 t 3 , 5 t + 3 t 2 + 7 t 3 } . What is the dimension of V ? Find a basis for V . 2. a) Find the eigenvalues of 3 5 16 4 0 3 11 0 0 15 1 0 0 4 1 2 . You do not need to find the eigenvectors. b) Find the eigenvalues and eigenvectors of parenleftbigg 3 8 2 3 parenrightbigg . 3. Consider the equations x 1 ( n + 1) = 2 x 1 ( n ) + 3 x 2 ( n ) x 2 ( n + 1) = 2 x 1 ( n ) + x 2 ( n ) a) If x (0) = parenleftbigg 1 0 parenrightbigg , what is x ( n )? b) If x (0) = parenleftbigg 0 1 parenrightbigg , what is x ( n )? c) Compute A n , where A = parenleftbigg 2 3 2 1 parenrightbigg . 4. Consider the nonlinear system of differential equations dx 1 dt = x 2 1 + x 1 x 2 4 x 1 + x 2 + 1 dx 2 dt = x 2 2 + x 1

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 ]}

### Page1 / 3

2009bfinweb - M346 Final Exam 1325 1 0 0 4/11 2 1 1 1 0 1 0...

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

View Full Document
Ask a homework question - tutors are online