e305k

# e305k - MAS 3105 Quiz 3 and Key May 26, 2005 Prof. S....

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MAS 3105 May 26, 2005 Quiz 3 and Key Prof. S. Hudson Name Show all your work and reasoning for maximum credit. If you continue your work on another page, be sure to leave a note. Do not use a calculator, book, or any personal paper. You may ask about any ambiguous questions or for extra paper. If you use extra paper, hand it in with your exam. 1) Answer True or False: If A is row equivalent to B , then det A = det B . If A is a nonsingular 3x3 matrix, then its columns form a basis of R 3 . P 2 is a subspace of P 3 . ( P 3 = the set of poly’s of degree < 3). Every square matrix is row equivalent to the identity or to a matrix with a row of zeroes. det ( A T A ) is always greater than or equal to 0. 2) Answer all three parts, based on the matrix A given below. a) Find adj A . b) Use the answer to a) to ﬁnd A - 1 . [ Don’t use G.E.] c) Find det A - 1 [Try to do this without using the answer to b)] A = 1 3 5 0 2 4 0 0 3 3) Choose ONE of these to prove. Assume that A and B are square nxn matrices. For

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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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e305k - MAS 3105 Quiz 3 and Key May 26, 2005 Prof. S....

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