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Back to The Linear Combination Lemma

Exercise 15

Avg difficulty 3.0

The Linear Combination Lemma says which equations can be gotten from Gaussian reduction of a given linear system.

  1. Produce an equation not implied by this system.

    3x+4y=82x+y=3\begin{array}{rcrcr}3x&+&4y&=&8\\ 2x&+&y&=&3\end{array}

  2. Can any equation be derived from an inconsistent system?

Hefferon, Linear Algebra, Linear Systems, The Linear Combination Lemma, Exercise 15

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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.