 # Describe what is meant by the augmented matrix of a system of linear equations. Nannie Mack 2020-11-17 Answered
Describe what is meant by the augmented matrix of a system of linear equations.
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Step 1
Describe what is meant by the augmented matrix of a system of linear equations.
Step 2
Let us consider a linear system of N equations in M unknowns ${A}_{11}{x}_{1}+{A}_{12}{x}_{2}+{A}_{13}{x}_{3}+\dots \dots ..+{A}_{1M}{x}_{M}={b}_{1}$ ${A}_{21}{x}_{1}+{A}_{22}{x}_{2}+{A}_{23}{x}_{3}+\dots \dots ..+{A}_{2M}{x}_{M}={b}_{2}$
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${A}_{N1}{x}_{1}+{A}_{N2}{x}_{2}+{A}_{N3}{x}_{3}+\dots \dots ..+{A}_{NM}{x}_{M}={b}_{N}$
represnted as , Ax=b where A is the $N×M$ matrix of coefficients,x is the $M×1$ vectors of unknowns and b is the $N×1$ vector of constantThe augmented matrix of the system is $\left(A\mid b\right)$ e.g, The system of two equations in two unknowns
$2{x}_{1}+{x}_{2}=1$
${x}_{1}+2{x}_{2}=3$
can be represented in matrix form as
Ax=b
where $A=\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right],x=\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}b=\left[\begin{array}{c}1\\ 3\end{array}\right]$
The augmented matrix of the system is
$⇒\left(A\mid b\right)=\left[\begin{array}{ccc}2& 1& 1\\ 1& 2& 3\end{array}\right]$