# solq3 - Solutions to quiz 3(September 23 1 Bringing the...

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Solutions to quiz # 3 (September 23) 1. Bringing the matrix to the 1 a 3 reduced row-echelon form, we obtain 11 1 1 1 2 4 −→ 0 2 − a 4 − a . 3a 0 0 a−3 If a = 2, 3 we can proceed further 1 1 1 1 0 2 − a 4 − a −→ 0 0 0 a−3 0 1 1 0 1 and the rank of the matrix is 3. If a = 2, we have the matrix 11 1 11 0 0 2 −→ 0 0 0 0 −1 00 and the rank of the matrix is 2. If a = 3, we have the matrix 11 0 −1 00 0 100 0 −→ 0 1 0 1 001 11 4−a −→ 0 1 2−a 1 00 1 10 −→ 0 1 1 0 00 0 1 0 2 −1 0 and the rank of the matrix is 2. Answer: The rank is 2 when a = 2 or when a = 3. 2. We observe that vector vector 1 0 is mapped to vector 0 −1 −1 . Hence the matrix of the transformation is 0 y 0 1 y=x −1 0 and vector 0 −1 1 0 x 0 0 −1 Answer: The matrix of the transformation is 1 0 −1 −1 . 0 −1 . 0 0 1 is mapped to ...
View Full Document

## This note was uploaded on 12/26/2011 for the course MATH 214 taught by Professor Conger during the Fall '08 term at University of Michigan.

Ask a homework question - tutors are online