math111hw7 - MATH111 HW 7 Due Date: 29th, Oct, 2007 (Mon)...

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Unformatted text preview: MATH111 HW 7 Due Date: 29th, Oct, 2007 (Mon) Please hand in your homework in the tutorial session or by putting it in the collection box outside MATH dept (Rm 3461, Lift 25-26). Ch 2.9 # 6 In the following exercise, the vector x is in a subspace H with a basis B = { b 1 , b 2 } . Find the B-coordinate vector of x . b 1 = - 3 1- 4 , b 2 = 7 5- 6 , x = 11 7 , Ch 2.9 # 10 In the following the matrix A and an echelon form of A is displayed. Find bases for Col A and Nul A , and then state the dimensions of these subspaces. A = 1- 2 9 5 4 1- 1 6 5- 3- 2- 6 1- 2 4 1 9 1- 9 ∼ 1- 2 9 5 4 1- 3- 7 1- 2 Ch 2.9 # 16 Suppose a 4 × 7 matrix A has three pivot columns. Is Col A = R 3 ? What is the dimension of Nul A ? Explain your answer. Ch 2.9 # 18 In the following exercise, mark each statement True or False. Justify each answer. Here A is an m × n matrix....
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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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math111hw7 - MATH111 HW 7 Due Date: 29th, Oct, 2007 (Mon)...

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