111-quiz2-sol

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

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

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

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