Purdue Linear Algebra Final

# Purdue Linear Algebra Final - MATH 265 FINAL EXAM Name and...

This preview shows pages 1–6. Sign up to view the full content.

MATH 265 FINAL EXAM Name and ID: Instructor: Section or class time: Instructions: Calculators are not allowed. There are 8 problems in the ﬁrst part worth 13 points each. There are 12 problems in the second part worth 8 points each. The total is 200 points. 1 2 3 4 5 6 7 8 9 x 10 x 11 x 12 x 1

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

View Full Document
Part I You must show all work for problems in ﬁrst part. 1. Let A = ± 0 a b c ² (a) Find conditions on a, b and c such that A is symmetric. (b) Find conditions on a, b and c such that A has an inverse. (c) Find conditions on a, b and c such that A satisﬁes A 2 = 0. 2
2. Consider a linear system whose augmented matrix is of the form 0 t - 7 0 6 0 2 2 t - 2 - 2 1 - 1 - 2 1 (a) For what values of t will the system have no solutions? (b) For what values of t will the system have inﬁnitely many solutions? 3

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

View Full Document
3. Find a basis for the subspace of R 4 spanned by v 1 = 0 2 3 0 , v 2 = 1 2 0 1 , v 3 = 1 0 - 3 1 , v 4 = 1 1 0 0 . 4
4. Let W be the span of (1 , 0 , 2) and (0 , 1 , 0) in R 3 (which is given the standard inner product.) (a) Find a basis for W .

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 / 21

Purdue Linear Algebra Final - MATH 265 FINAL EXAM Name and...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online