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Back to Gauss’s Method

Exercise 4

Avg difficulty 3.0

Solve each system or conclude ‘many solutions’ or ‘no solutions’. Use Gauss’s Method.

  • (a)  x+y+z=5x−y=0y+2z=7\begin{array}{rcrcrcr}x&+&y&+&z&=&5\\ x&-&y&&&=&0\\ &&y&+&2z&=&7\end{array}     (b)  3x+z=7x−y+3z=4x+2y−5z=−1\begin{array}{rcrcrcr}3x&&&+&z&=&7\\ x&-&y&+&3z&=&4\\ x&+&2y&-&5z&=&-1\end{array}     (c)  x+3y+z=0−x−y=2−x+y+2z=8\begin{array}{rcrcrcr}x&+&3y&+&z&=&0\\ -x&-&y&&&=&2\\ -x&+&y&+&2z&=&8\end{array}

Hefferon, Linear Algebra, Linear Systems, Gauss’s Method, Exercise 4

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.