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# Week1 - 1 0 Next we subtract three times row two from row...

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Solutions for Assignment 1 Applied Linear Algebra MATH 232 (Fall 2008) Section 1.1 Section 1.2

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Section 1.3
Assignment 1 Applied Linear Algebra Math 232(Fall 2008) Additional question: For which values of h does the system of equations below have more than one solution? x 1 + x 2 + x 3 = 0 x 1 + 2 x 2 + hx 3 = 0 x 1 + 4 x 2 + h 2 x 3 = 0 . A1. We create the augmented matrix 1 1 1 0 1 2 h 0 1 4 h 2 0 . We row reduce, first subracting row one from row two and then subtracting row one from row three, to obtain 1 1 1 0 0 1 h - 1 0 0 3 h 2 - 1 0 . Next we subtract three times row two from row three to obtain
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Unformatted text preview: 1 0 . Next we subtract three times row two from row three to obtain 1 1 1 0 1 h-1 0 0 h 2-3 h + 2 0 . Observe that x 1 and x 2 are not free variables since there are pivots in the ﬁrst and second column. The variable x 3 is free if and only if h 2-3 h + 2 = 0. Factoring, we see if h = 2 or h = 1 then we have a free variable and hence the system has more than one solution in these cases. 1...
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Week1 - 1 0 Next we subtract three times row two from row...

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