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Exercises Systems of equations

Example 1 from Algebra and Trigonometry, 11.6 Solving Systems with Gaussian Elimination

Writing the Augmented Matrix for a System of Equations

Write the augmented matrix for the given system of equations.

\begin{array}{l} x + 2 y - z = 3 \\ 2x-y+2z=6 \\ x - 3 y + 3 z = 4 \end{array}

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The augmented matrix displays the coefficients of the variables, and an additional column for the constants.

$[\begin{array}{r} 1 & 2 & −1 \\ 2 & −1 & 2 \\ 1 & −3 & 3 \end{array} | \begin{array}{r} 3 \\ 6 \\ 4 \end{array}]$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write the augmented matrix of the given system of equations.

\begin{array}{l} 4 x −3 y = 11 \\ 3 x + 2 y = 4 \end{array}

How did it go?

PreviousUsing a Calculator to Perform Matrix Operations Next Writing a System of Equations from an Augmented Matrix Form

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 11.6, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.