wksht08sol - MATH 152 L1 & L2 Applied Linear Algebra...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 152 L1 & L2 Applied Linear Algebra and Differential Equations Spring 2004-05 ¥ Week 08 Worksheet Solutions : Matrix Q1. (Addition and scalar multiplication) Solve 3 A- • 3 1 2 2 ‚ = •- 3 2 4- 2 ‚ . Solution 3 A = •- 3 2 4- 2 ‚ + • 3 1 2 2 ‚ = • 3 6 ‚ , A = 1 3 • 3 6 ‚ = • 1 2 ‚ . Q2. (Matrix multiplication) Simplify A [(3 A- 7 B )- (7 A + 2 B )]- ( A- 2 B ) B . Solution A [(3 A- 7 B )- (7 A + 2 B )]- ( A- 2 B ) B = A (3 A- 7 B- 7 A- 2 B )- ( AB- 2 B 2 ) = A (- 4 A- 9 B )- AB + 2 B 2 =- 4 A 2- 9 AB- AB + 2 B 2 =- 4 A 2- 10 AB + 2 B 2 . Q3. (Matrix equation) Let A = • 1 y- y 2 x ‚ and B = • x- 2 x y 2 ‚ . Find x , y such that BA = O . Solution Note that BA = • x + 2 xy- 4 x 2 + xy- y 4 x + y 2 ‚ . Then BA = O is equivalent to x + 2 xy = 0 ,- 4 x 2 + xy = 0 ,- y = 0 , 4 x + y 2 = 0 . From the third equation, we have y = 0. Then the first equation becomes x + 0 = 0, i.e., x = 0. Conversely, if x = y = 0, then all four equations are satisfied. Hence, BA = O if and only if x = y = 0....
View Full Document

This note was uploaded on 09/30/2010 for the course MATH MATH152 taught by Professor Kcc during the Spring '10 term at HKUST.

Page1 / 3

wksht08sol - MATH 152 L1 & L2 Applied Linear Algebra...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online