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Exercises Systems of equations

Example 3 from Algebra and Trigonometry, 11.5 Matrices and Matrix Operations

Adding Matrix A and Matrix B

Find the sum of $A$ and $B .$

A = [\begin{matrix} 4 & 1 \\ 3 & 2 \end{matrix}] and B = [\begin{matrix} 5 & 9 \\ 0 & 7 \end{matrix}]

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
Add corresponding entries. Add the entry in row 1, column 1, $a_{11},$ of matrix $A$ to the entry in row 1, column 1, $b_{11},$ of $B .$ Continue the pattern until all entries have been added.
$\begin{array}{l} A + B = [\begin{matrix} 4 & 1 \\ 3 & 2 \end{matrix}] + [\begin{matrix} 5 & 9 \\ 0 & 7 \end{matrix}] \\ = [\begin{matrix} 4 + 5 & 1 + 9 \\ 3 + 0 & 2 + 7 \end{matrix}] \\ = [\begin{matrix} 9 & 10 \\ 3 & 9 \end{matrix}] \end{array}$

How did it go?

PreviousFinding the Sum of Matrices Next Finding the Difference of Two Matrices

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 11.5, 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.