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Exercise 11

Avg difficulty 3.0

  • Apply Gauss’s Method to the left-hand side to solve

    x+2y−w=a2x+z=bx+y+2w=c\begin{array}{rcrcrcrcr}x&+&2y&&&-&w&=&a\\ 2x&&&+&z&&&=&b\\ x&+&y&&&+&2w&=&c\end{array}

    for xx, yy, zz, and ww, in terms of the constants aa, bb, and cc.

  • Use your answer from the prior part to solve this.

    x+2y−w=32x+z=1x+y+2w=−2\begin{array}{rcrcrcrcr}x&+&2y&&&-&w&=&3\\ 2x&&&+&z&&&=&1\\ x&+&y&&&+&2w&=&-2\end{array}

Hefferon, Linear Algebra, Linear Systems, Describing the Solution Set, Exercise 11

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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.