QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
# MATH 1324 - Homework \#2
Complete all work neatly on your own paper and not on this assignment sheet itself. All steps should be shown and your work must be easily readable. Problems without work or explanation will receive no credit. You will be turning in all homework online through D^2L.
## Matrix Arithmetic
Evaluate the following matrix operations, or state that there is no solution and explain why not.
1) $\left[\begin{array}{ll}3 & 1 \\ 5 & 2 \\ 10 & 4\end{array}\right]+\left[\begin{array}{ll}6 & 7 \\ 0 & 8 \\ 9 & 1\end{array}\right]$
2) $\left[\begin{array}{ll}22 & 35 \\ 48 & 62\end{array}\right]+\left[\begin{array}{ll}14 & 27 \\ 55 & 28\end{array}\right]$
3) $\left[\begin{array}{lll}11 & 22 & 33 \\ 44 & 55 & 66\end{array}\right]-\left[\begin{array}{lll}9 & 8 & 7 \\ 6 & 5 & 2\end{array}\right]$
4) $\left[\begin{array}{lll}16 & 14 \\ 12 & 10 \\ 28 & 26\end{array}\right]-\left[\begin{array}{lll}13 & 12 & 11 \\ 9 & 12 & 15\end{array}\right]$
5) $5\left[\begin{array}{cc}4 & 8 \\ - 7 & 13\end{array}\right]$
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Answer
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Step 1: Add the matrices together.
\left[\begin{array}{ll}3 & 1 \ 5 & 2 \ 10 & 4\end{array}\right]+\left[\begin{array}{ll}6 & 7 \ 0 & 8 \ 9 & 1\end{array}\right] = \left[\begin{array}{ll}3+6 & 1+7 \ 5+0 & 2+8 \ 10+9 & 4+1\end{array}\right] = \boxed{\left[\begin{array}{ll}9 & 8 \ 5 & 10 \ 19 & 5\end{array}\right]}
To do this, add the corresponding entries.
Step 2: Add the matrices together.
\left[\begin{array}{ll}22 & 35 \ 48 & 62\end{array}\right]+\left[\begin{array}{ll}14 & 27 \ 55 & 28\end{array}\right] = \left[\begin{array}{ll}22+14 & 35+27 \ 48+55 & 62+28\end{array}\right] = \boxed{\left[\begin{array}{ll}36 & 62 \ 103 & 90\end{array}\right]}
To do this, add the corresponding entries.
Final Answer
5\left[\begin{array}{cc}4 & 8 \ - 7 & 13\end{array}\right] = \left[\begin{array}{cc}5\times^4 & 5\times^8 \ 5\times- 7 & 5\times^13\end{array}\right] = \boxed{\left[\begin{array}{cc}20 & 40 \ - 35 & 65\end{array}\right]}
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