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Exercises Systems of equations

Example 5 from Algebra and Trigonometry, 11.5 Matrices and Matrix Operations

Finding the Sum and Difference of Two 3 x 3 Matrices

Given $A$ and $B :$

ⓐFind the sum.
ⓑFind the difference.

A = [\begin{array}{r} 2 & −10 & −2 \\ 14 & 12 & 10 \\ 4 & −2 & 2 \end{array}] and B = [\begin{array}{r} 6 & 10 & −2 \\ 0 & −12 & −4 \\ −5 & 2 & −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.

1
Solution
1. ⓐAdd the corresponding entries.
  $\begin{array}{l} A + B = [\begin{array}{r} 2 & - 10 & - 2 \\ 14 & 12 & 10 \\ 4 & - 2 & 2 \end{array}] + [\begin{array}{r} 6 & 10 & - 2 \\ 0 & - 12 & - 4 \\ - 5 & 2 & - 2 \end{array}] \\ = [\begin{array}{r} 2 + 6 & - 10 + 10 & - 2 - 2 \\ 14 + 0 & 12 - 12 & 10 - 4 \\ 4 - 5 & - 2 + 2 & 2 - 2 \end{array}] \\ = [\begin{array}{r} 8 & 0 & - 4 \\ 14 & 0 & 6 \\ - 1 & 0 & 0 \end{array}] \end{array}$
2. ⓑSubtract the corresponding entries.
  $\begin{array}{l} A - B = [\begin{array}{r} 2 & −10 & −2 \\ 14 & 12 & 10 \\ 4 & −2 & 2 \end{array}] - [\begin{array}{r} 6 & 10 & −2 \\ 0 & −12 & −4 \\ −5 & 2 & −2 \end{array}] \\ = [\begin{array}{r} 2 - 6 & −10 - 10 & −2 + 2 \\ 14 - 0 & 12 + 12 & 10 + 4 \\ 4 + 5 & −2 - 2 & 2 + 2 \end{array}] \\ = [\begin{array}{r} −4 & −20 & 0 \\ 14 & 24 & 14 \\ 9 & −4 & 4 \end{array}] \end{array}$

Your turn

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

Add matrix $A$ and matrix $B .$

A = [\begin{array}{r} 2 & 6 \\ 1 & 0 \\ 1 & −3 \end{array}] and B = [\begin{array}{r} 3 & −2 \\ 1 & 5 \\ −4 & 3 \end{array}]

How did it go?

PreviousFinding the Difference of Two Matrices Next Multiplying the Matrix by a Scalar

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.