Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 10 - Systems of Equations and Inequalities - Section 10.2 Systems of Linear Equations: Matrices - 10.2 Assess Your Understanding - Page 749: 8


$[A|B]=\left[\begin{array}{rr|r} {9}&{-1} &{ 0 }\\ {3}&{-1} &{4 }\end{array}\right]$

Work Step by Step

The standard form of a linear equation can be expressed as: $$a_{i1}x_{1}+a_{i2}x_{2}+...+a_{in}x_{n}=b_{i}$$ where the index $i$ indicates that it is the i-th equation of a system of equations. In order to write the augmented matrix $[A|B]$ of a system of equations in standard form, we must follow some important points: 1. To express a system in matrix form, we must extract the coefficients of the variables and constants. 2. Draw a vertical line to separate the coefficient entries from the constants (essentially replacing the equal signs). 3. The entries of the coefficient matrix $A=[a_{ij}]$ must be placed to the left of the lline. 4. The constants of the $B=[b_{i}]$ must be placed to the right of the line. We rewrite the system in standard form as: $9x-y=0 \\3x-y=4$ Now, we have: $ A=\left[\begin{array}{ll} 9 & -1\\ 3 & -1 \end{array}\right] $ and $B=\left[\begin{array}{l} 0\\4\end{array}\right]$ Finally, we can write the system as an augmented matrix $[A|B]$ as follows: $[A|B]=\left[\begin{array}{rr|r} {9}&{-1} &{ 0 }\\ {3}&{-1} &{4 }\end{array}\right]$
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