Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.4 Exercises - Page 40: 6

Answer

$$ -2 \begin{bmatrix} 7\\2\\9\\-3 \end{bmatrix} -5 \begin{bmatrix} -3\\1\\-6\\2 \end{bmatrix} = \begin{bmatrix} 1\\-9\\12\\-4 \end{bmatrix} $$

Work Step by Step

From the definition of matrix-vector multiplication, we can expand the product. Since there are two columns, it is the equivalent of multiplying the first entry of the vector ($-2$) by the first column of the matrix, and doing the same for the second entry and column. We sum them together (this is the definition of matrix-vector multiplication), and the product equals the right hand side of the equation provided.
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