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Exercises Systems of equations

Example 9 from Algebra and Trigonometry, 11.7 Solving Systems with Inverses

Using a Calculator to Solve a System of Equations with Matrix Inverses

Solve the system of equations with matrix inverses using a calculator

\begin{array}{l} 2 x + 3 y + z = 32 \\ 3 x + 3 y + z = −27 \\ 2 x + 4 y + z = −2 \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
On the matrix page of the calculator, enter the coefficient matrix as the matrix variable $[A],$ and enter the constant matrix as the matrix variable $[B] .$
$[A] = [\begin{matrix} 2 & 3 & 1 \\ 3 & 3 & 1 \\ 2 & 4 & 1 \end{matrix}], [B] = [\begin{matrix} 32 \\ −27 \\ −2 \end{matrix}]$

On the home screen of the calculator, type in the multiplication to solve for $X,$ calling up each matrix variable as needed.

${[A]}^{−1} \times [B]$

Evaluate the expression.

$[\begin{matrix} −59 \\ −34 \\ 252 \end{matrix}]$

How did it go?

PreviousSolving a 3 × 3 System Using the Inverse of a Matrix Next Finding the Determinant of a 2 × 2 Matrix

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 11.7, 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.