Q1-Sol.pdf - Computational Linear Algebra-MAS 3114 NAME...

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Computational Linear Algebra-MAS 3114 NAME: QUIZ #1 Show all of your work to get full credit. 1. Use Elementary Row Operations to Row-reduce the following system so that the leftmost variable in each row has a coefflcient 1 in the reduced form: \\ x x 2x + y 4- 3z ==8 x + y - 4z = 5 1 ^ "^ f ^ ^ ^,^¥z ^ I -^ 1 8 ^ ' J \ \ - 4- 1 5 r 1 c/^ o ~i \\ \ ~z.^^^^^ ^ - X ^ LJ ^ 4.^ ^ ^ ^ ^> R ^ +L)^H ^& \'< >^ ^ •^ +- ^ -A'i, ^ ^ -tl +n^-. ^-^R.^. ^, \\ )c v \ -^ 0 I - ll ^r^l/J '\/ ,., € :--" I x or / 'x ^ u) - ^3- ^ ^ \ (j - U^ ^ Z- y^^ N\- \\ Y ^ ^ \ ^ 107 1-7 0 \ -\\ \ Z // 0-^- •>L +7^-7 C-n^-^ ^ -n^ - •.> -^^ 2. Find all values of a for which this linear system has no solution. x " y + 3z = 1 3x + 2y - z == 4 2x - 2y + (<32+5)z = ri?+3 •^ - 'A + Z-^ -- *' 5^ - 1^ •= \ Q-3-)t3,+R^ (c^Q ^ ^ o.+\ (c^)^^ ^3 v ^L ^ \^ ?c (^-OQo<+<) ^ i/j^ g^A- 0=1^ t^V\^c^ \s ^ c^rW ol^c^^^
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