Math121 - Extra Problems Week 4-5

# Math121 - Extra Problems Week 4-5 - MATH 121 DISCUSSION...

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MATH 121 DISCUSSION WEEK 4-5 EXTRA PROBLEMS 1) How do we know that the system of equations below has an inﬁnite number of solutions? x + 3 y + 4 z = 2 2 y - 6 z = 4 - y + 3 z = - 2 2) How do we know that the system of equations below has an inﬁnite number of solutions? x - 7 y 9 w = - 11 2 x + y - 3 z + w = 13 3) How do we know that the system of equations below has no solutions? x - 5 y + 7 z = 3 y + 4 z = 9 3 x + 12 z = 2 4) Consider the below matrices A = ± 1 - 3 - 3 9 ² ,B = ± 2 5 1 2 ² (a) Solve ( A + B ) - 3 A . (b) Solve 2 A - B . (c) Solve AB . (d) Show that A - 1 does not exist. (e) Find B - 1 . (f) Show that you found the correct B - 1 in part (e) by verifying that B - 1 B = I . 5) Consider the below system of equations. x - 3 y = 11 - 2 x + 5 y = - 4 (a) Rewrite the system as a matrix equation of the form AX = B . (b) Using A - 1 , solve the system of equations. 6) Consider the below system of equations. 4

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## This note was uploaded on 12/07/2010 for the course MATH Math 121 taught by Professor Beaulieu during the Fall '10 term at UMass (Amherst).

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Math121 - Extra Problems Week 4-5 - MATH 121 DISCUSSION...

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