MidSol2 - Comparing corresponding entries in the rst...

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

View Full Document Right Arrow Icon
Comparing corresponding entries in the frst column, we obtain a + b 3= a c 3 and c + d a 3+ c , which gives b = c and d = a . In that case entries in the second column are automatically equal. We conclude that B has the Form B = µ a c ca For arbitrary numbers a and c . As in class we conclude that this matrix represents the composition oF a rotation and a dilation. To see this, it is enough to take r = a 2 + c 2 , and fnd an angle θ so that a = r cos θ , c = r sin θ . Then we have: B = µ r 0 0 r ¶µ cos θ sin θ sin θ cos θ . 4. We perForm the algorithm given in class: 111 | 100 320 | 010 001 | subtract 3 times row I From row II 11 1 | 0 1 3 |− 310 00 1 | multiply row II by 1 | 013 | 3 10 | subtract row II From row I 2 210 01 3 | 3
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/12/2011 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.

Ask a homework question - tutors are online