Chapter 1 & 3 Test B Keys

Chapter 1 & 3 Test B Keys - R 6 (7c) Exactly one...

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Math 211: Linear Algebra Midterm 2 Review Chapter 1 Test B (3a) Infinitely many (3b) A is singular (5a) E = 1 0 0 0 0 1 0 1 0 (6) Yes, (3 , 1 , 4) T is a solution (7) A is singular (8) Yes, let A = ± 1 4 1 4 ² and B = ± 2 3 2 3 ² (10) Yes, since C = EF is the product of two invertible matrices Chapter 3 Test B (1) No, the vectors are linearly dependent (3a) { ( - 3 , 1 , 0 , 0 , 0) T , ( - 2 , 0 , - 1 , 1 , 0) T , ( - 3 , 0 , - 1 , 0 , 1) T } is a basis for N ( A ) (3b) { (1 , 0 , 0 , 0) T , (1 , 1 , 2 , 3) T } is a basis for Col( A ) (4) dim Col( A ) = # lead variables, and dim N ( A ) = # free variables (5a) Yes (5b) No, see 3.4.17 (6) see 3.4.12f (7a) dim N ( A ) = 0 and dim Col( A ) = 4 (7b) The column vectors are linearly independent, but they do not span
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Unformatted text preview: R 6 (7c) Exactly one solution (8a) Linearly dependent (8b) No, they do not span R 3 (8c) They are linearly dependent, and therefore neither span R 3 nor form a basis for R 3 (8d) They are linearly independent, and therefore span R 3 and form a basis for R 3 (9) see 3.3.17 (10a) dim N ( A ) = 2 (10b) RREF ( A ) = 1 0 0 1 2 0 1 0 3 0 0 1 1-1 0 0 0 0 0 0 0 0 0 0 0 0 (11a) U-1 = ± 7-2-3 1 ² (11b) UV-1 = ± 31 10-13-3 ² 1...
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This document was uploaded on 06/10/2011.

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