Chp3Quiz

Chp3Quiz - Math 330 Chapter 3 Quizzes Section 3.1 Take home...

This preview shows pages 1–3. Sign up to view the full content.

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.

Unformatted text preview: Math 330 Chapter 3 Quizzes Section 3.1 - Take home assigned February 18, 2009 Suppose that A and the product AB are as given below. Determine B A = bracketleftBigg 1- 1 3 bracketrightBigg AB = bracketleftBigg 2- 2 0 0 6 0 1 bracketrightBigg SOLUTION: Since A is 2 × 2 and AB is 2 × 4 it must mean that B is 2 × 4. The 4 columns of AB come from come from linear combinations of the columns of A . Each column of B gives weights to produce the resulting column of AB . Let vectora 1 and vectora 2 denote the first and second columns respectively of A . Then we note the following about the columns vector c 1 ,vector c 2 ,vector c 3 , and vector c 4 of AB : • By inspection vector c 1 = 2 vectora 1 + 0 vectora 2 . • By inspection vector c 2 = 0 vectora 1 + 2 vectora 2 • By inspection vector 0 = vector c 3 = 0 vectora 1 + 0 vectora 2 • We can find the last column vectorx of B by solving the system Avectorx = vector c 4 : bracketleftBigg 1- 1 3 bracketrightBiggbracketleftBigg b 14 b 24 bracketrightBigg = bracketleftBigg 1 bracketrightBigg = ⇒ bracketleftBigg 1- 1 0 3 1 bracketrightBigg R 2 ← R 2- 3 R 1 = ⇒ bracketleftBigg 1- 1 0 3 1 bracketrightBigg R 2 ← R 2 3 = ⇒ bracketleftBigg 1- 1 0 1 1 3 bracketrightBigg R 1 ← R 1+ R 2 = ⇒ bracketleftBigg 1 0 1 3 0 1 1 3 bracketrightBigg So we have that vector c 4 = 1 3 vectora 1 + 1 3 vectora 2 . Therefore, B = bracketleftBigg 2 0 0 1 3 0 2 0 1 3 bracketrightBigg Section 3.2 February 20, 2009 Without the use of technology, show all the steps needed to calculate A- 1 : A = 1 1 1- 1 1- 2- 1 0- 1 SOLUTION: We triply augment A using I 3 and we reduce A to reduced Echelon form which (in this case) will be I 3 : 1 1 1 1 1 0 0- 1 1- 2 0 1 0- 1 0- 1 0 0 1 R 2 ← R 2+ R 1 & R 3 ← R 3+ R 1 = ⇒ 1 1 1 1 0 0 0 2- 1 1 1 0 0 1 1 0 1 R 2 ↔ R 3 = ⇒ 1 1 1 1 0 0 0 1 1 0 1 0 2- 1 1 1 0 R 3 ← R 3- 2 R 2 = ⇒ 1 1 1 1 0 1 1 1 0 0- 1- 1 1- 2 R 3 ←- R 3 = ⇒ 1 1 1 1 0 1 0 1 1 0 0 1 1- 1 2 This completes the reduction to Echelon form. We then continue to reduced Echelon form R 1 ← R 1- R 2 = ⇒ 1 0 1 0- 1 0 1 0 1 1 0 0 1 1- 1 2 R 1 ← R 1- R 3 = ⇒ 1 0 0- 1 1- 3 0 1 0 1 1 0 0 1 1- 1 2 Therefore, A- 1 = - 1 1- 3 1 1 1- 1 2 Section 2.3 Take-home assigned February 23, 2009 Suppose that A is a 4 × 4 matrix with the following properties: • A is invertible. • A 1 2 3 4 = vectorv 1 = 1 1 1 1 • A 1- 2- 3 4 = vectorv 2 = 1 1 1 • A 4 3 2 1 = vectorv 3 = 1 1 1 1. 2 points Find a linear combination of vectorv 1 ,vectorv 2 ,vectorv 3 which produces...
View Full Document

This note was uploaded on 09/19/2009 for the course MATH 330 taught by Professor Johnson,j during the Spring '08 term at Nevada.

Page1 / 8

Chp3Quiz - Math 330 Chapter 3 Quizzes Section 3.1 Take home...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online