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Exercise 17

Avg difficulty 3.0

Show that this set of column vectors

{(d1d2d3)∣there are x, y, and z such that: 3x+2y+4z=d1x−z=d22x+2y+5z=d3}\{\hskip 1.00006pt\begin{pmatrix}d_{1}\\ d_{2}\\ d_{3}\end{pmatrix}\mid\text{there are $x$, $y$, and $z$ such that:\ }\begin{array}{rcrcrcr}3x&+&2y&+&4z&=&d_{1}\\ x&&&-&z&=&d_{2}\\ 2x&+&2y&+&5z&=&d_{3}\end{array}\hskip 1.00006pt\}

is a subspace of R3\mathbb{R}^{3}. Find a basis.

Hefferon, Linear Algebra, Vector Spaces, Vector Spaces and Linear Systems, Exercise 17

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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.