Chapter 8, Problem 6RE

To determine

Find the augmented matrix of given linear equations

Answer to Problem 6RE

The augmented matrix has three rows and four columns, so it is 3×4 matrix

Explanation of Solution

Given:

System of linear equations,

  $\{\begin{array}{l}8x–7x+4z=12\hfill \\ 3x–5y+2z=20\hfill \\ 5x+3y–3z=26\hfill \end{array}$

Consider the following system of linear equations,

  $\{\begin{array}{l}8x–7x+4z=12\hfill \\ 3x–5y+2z=20\hfill \\ 5x+3y–3z=26\hfill \end{array}$

In general, the augmented matrix for any system of linear equations that has m number of equations and n number of variables, then it's augmented matrix is,

  $\left[\begin{array}{ccccc}{a}_{11}& \cdots & a_{1m}& ⋮& k_1\\ ⋮& \ddots & & ⋮& \\ a_{m1}& \cdots & a_{mn}& ⋮& k_m\end{array}\right]$

Use the coefficients and constant terms as the matrix elements. Take zero for missing variable.

Then augmented matrix is,

  $\begin{array}{c}{R}_1\\ R_2\\ R_3\end{array}\left[\begin{array}{ccccc}8& -7& 4& ⋮& 12\\ 3& 5& 2& ⋮& 20\\ 5& 3& -3& ⋮& 26\end{array}\right]$

Thus augmented matrix has three rows and four columns, so it is 3×4 matrix.