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Exercise 4

Avg difficulty 3.0

For the system

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

which of these can be used as the particular solution part of some general solution?

  • (a)  (0−350)\begin{pmatrix}0\\ -3\\ 5\\ 0\end{pmatrix}     (b)  (2110)\begin{pmatrix}2\\ 1\\ 1\\ 0\end{pmatrix}     (c)  (−1−48−1)\begin{pmatrix}-1\\ -4\\ 8\\ -1\end{pmatrix}

Hefferon, Linear Algebra, Linear Systems, General=Particular+Homogeneous, 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.