Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 0-32198-238-X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.7 Exercises: 26

Answer

$ \begin{bmatrix} \blacksquare&*&*\\ 0&\blacksquare&*\\ 0&0&\blacksquare\\ 0&0&0 \end{bmatrix} $

Work Step by Step

If the first two vectors in the set are linearly independent, and the third vector is not a linear combination of the first two, then by Theorem 7, the three vectors must be linearly independent. Hence, the only possibility is to have a pivot in each column, leaving the final row with all zeros.
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