Math 20FFirst MidtermJanuary 27, 2003•PRINT NAME•Write version on your blue book andVERSION Ahand 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. (4 pts.) Fill in the following blanks.(a) IfAis ann×nmatrix and there is a matrixBsuch that, we callBtheinverse ofA.(b) IfAandBare matrices such thataij=bjifor alliandj, we callB.2. (15 pts.) LetA=10-100001110-12203.(a) How many solutions doesAx= (1 0 0 0)Thave? Justify your answer.(b) How many solutions doesAx= (0 0 0 1)Thave? Justify your answer.(c) Either find abso thatAx=bhas exactly one solution or explain why this isimpossible.3. (10 pts.) Prove or give a counterexample:
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