HW4_solutions

HW4_solutions - Math 167 homework 4 solutions 2.4.2 Find...

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Unformatted text preview: Math 167 homework 4 solutions October 31, 2010 2.4.2: Find the dimension and construct a basis for the four subspaces as- sociated with each of the matrices A = bracketleftbigg 0 1 4 0 0 2 8 0 bracketrightbigg and U = bracketleftbigg 0 1 4 0 0 0 0 0 bracketrightbigg Matrix A : 1. dim C ( A ) = 1, basis is braceleftbiggbracketleftbigg 1 2 bracketrightbiggbracerightbigg 2. dim N ( A ) = n- r = 4- 1 = 3, basis is 1 , 1 , 4- 1 3. dim C ( A T ) = 1, basis is 1 4 4. dim N ( A T ) = m- r = 2- 1 = 1, basis is braceleftbiggbracketleftbigg 2- 1 bracketrightbiggbracerightbigg Matrix U : 1. dim C ( U ) = 1, basis is braceleftbiggbracketleftbigg 1 bracketrightbiggbracerightbigg 1 2. dim N ( U ) = n- r = 4- 1 = 3, basis is 1 , 1 , 4- 1 3. dim C ( U T ) = 1, basis is 1 4 4. dim N ( U T ) = m- r = 2- 1 = 1, basis is braceleftbiggbracketleftbigg 1 bracketrightbiggbracerightbigg 2.4.18: Find a basis for each of the four subspaces of A = 0 1 2 3 4 0 1 2 4 6 0 0 0 1 2 = 1 0 0 1 1 0 0 1 1 0 1 2 3 4 0 0 0 1 2 0 0 0 0 0 1. ( C ( A ))’s basis is...
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HW4_solutions - Math 167 homework 4 solutions 2.4.2 Find...

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