e204k - MAS 3105 Quiz 2 Key Feb 2 2004 Prof S Hudson 1[15pt...

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MAS 3105 Feb 2, 2004 Quiz 2 Key Prof. S. Hudson 1) [15pt] Find the determinants of these matrices. If possible, find quick ways to do them (without using the definition) and explain briefly. A = 1 2 3 0 5 6 0 0 7 B = 0 0 7 0 5 6 1 2 3 C = 1 2 1 2 3 2 1 2 1 2) [10pt] Show how you would enter the matrix A from problem 1) into Matlab. 3) [15pt] Find the D - 1 quickly (without GE) using clues hidden in the equation below. Think about how multiplication relates to rows and columns. Check your answer by multiplying out. DF = 1 0 2 3 1 3 11 3 14 1 - 2 4 5 6 2 3 5 - 9 - 8 3 1 6 - 2 - 3 = 7 0 16 1 0 14 0 35 0 1 59 1 143 0 0 = G 4) [20pt] Choose ONE of these to prove. You can answer on the back. a) If A is nonsingular then it is row equivalent to A - 1 . [You can quote theorems or results from HW to give a very short proof] b) If A is any mxn matrix, then A + A T is symmetric. c) Prove this part of Thm 1.4.3: If
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e204k - MAS 3105 Quiz 2 Key Feb 2 2004 Prof S Hudson 1[15pt...

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