e508k - MAS 3105 Quiz 5 AM: March 13, 2008 Prof. S. Hudson...

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MAS 3105 AM: March 13, 2008 Quiz 5 Prof. S. Hudson 1) Answer TRUE or FALSE: [the ‘ A ’ in part b) is not the same as in c), and so on] a) Two row equivalent matrices must have the same rank and the same nullity. b) A x = b is consistent if and only if b is in the column space of A . c) If A is a transition matrix, then A is square and det A 6 = 0 d) The rank of A is greater than or equal to the number of columns of A . e) If A represents L : R 3 R 2 then A is a 2x3 matrix. 2) These two matrices are row equivalent: A = 1 2 0 3 0 1 2 1 3 1 2 4 0 6 7 and U = 1 2 0 3 0 0 0 1 0 0 0 0 0 0 1 . a) Find a basis of the row space of A . b) Find a basis for the column space of A . c) Find a basis for the nullspace of A . d) Find the rank of A . e) Find the nullity of A . 3) Choose ONE of these. A) Let L be the operator on P 3 defined by L ( p ( x )) = xp 00 ( x ) + p (1). Find the matrix A representing L with respect to [1 ,x,x 2 ]. B) State and prove Theorem 5.1.1, the formula for the dot product which includes
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This note was uploaded on 12/26/2011 for the course MAS 3105 taught by Professor Julianedwards during the Spring '09 term at FIU.

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e508k - MAS 3105 Quiz 5 AM: March 13, 2008 Prof. S. Hudson...

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