111-quiz2-sol

111-quiz2-sol - MATH111 Quiz 2B Solution 1 Let T R83 R38 be...

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

MATH111 Quiz 2B Solution 1. Let T : R 83 R 38 be a linear transformation with standard matrix A . Determine if T is one-to-one; or onto; or both one-to-one and onto; or both are not one-to-one or onto; or just impossible. a. A has 83 pivot positions. Impossible b. A has 18 pivot positions. Not one-to-one or onto c. A has 38 pivot positions. Onto Explanation: A is 38 × 83, so the maximum number of pivot positions is 38. So a) is impossible. If A has 38 pivot positions that means every row has a pivot position, which implies A is onto. If A has 18 pivot positions, then every row and column of A cannot have at least 1 pivot position. So A is not one-to-one and onto. 2. Find the inverse of 1 2 1 - 1 1 3 1 1 2 using the algorithm [ A I ] [ I A - 1 ]. (Using another methods will give you 0 mark!) Consider [ A I ] = 1 2 1 1 0 0 - 1 1 3 0 1 0 1 1 2 0 0 1 1 2 1 1 0 0 0 3 4 1 1 0 0 - 1 1 - 1 0 1 1 2 1 1 0 0 0 - 1 1 - 1 0 1 0 3 4 1 1 0 1 2

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.

This note was uploaded on 04/03/2010 for the course MATH math111 taught by Professor Cheng during the Spring '07 term at HKUST.

Page1 / 2

111-quiz2-sol - MATH111 Quiz 2B Solution 1 Let T R83 R38 be...

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

View Full Document
Ask a homework question - tutors are online