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 41: 9

Answer

Vector equation: $$ x_1 \begin{bmatrix} 3\\0 \end{bmatrix} + x_2 \begin{bmatrix} 1\\1 \end{bmatrix} + x_3 \begin{bmatrix} -5\\4 \end{bmatrix} = \begin{bmatrix} 9\\0 \end{bmatrix} $$ Matrix equation: $$ \begin{bmatrix} 3&1&-5\\ 0&1&4 \end{bmatrix} \begin{bmatrix} x_1\\x_2\\x_3 \end{bmatrix} = \begin{bmatrix} 9\\0 \end{bmatrix} $$

Work Step by Step

We convert the system of equations into a vector equation with the same variables above. The first entries of the vectors corresponds to the coefficients of the variables in the first equation; the second entries correspond to the second equation. The matrix equation is formed by putting all the vectors as the column of a matrix and multiplying them by a vector holding the coefficients in the vector equation.
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