Math 20FFirst MidtermJanuary 27, 2003•PRINT NAME•Write version on your blue book andVERSION Bhand in this exam inside your blue book.•There are a total of 40 points possible.•No BOOKS, NOTES or CALCULATORS are allowed.•You must show your work to receive credit.1. (10 pts.) Prove or give a counterexample:(a) IfAandBare 2×2 matrices, thenAB=BA.(b) For every matrix matrixA, the ﬁrst entry inATAis non-negative.(In other words, ifB=ATA, thenb11≥0.)2. (15 pts.) LetA=11-1022 3 010 0-100 1 0.(a) How many solutions doesAx=(0100)Thave? Justify your answer.(b) How many solutions doesAx=(0010)Thave? Justify your answer.(c) Either ﬁnd abso thatAx=bhas exactly one solution or explain why this is
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