1. ## Matrices

I am going crazy. it is almost 3:00 in the morning and I have been trying to figure out a problem and I just can't get it.

If you could show me how I would so appreciate it. Iam taking an online math class and the teacher has 7 other classes and never seems to answer the questions on time. Thank you so much!

A =
• 2 0 1
• 2 -1 3
• 4 1 2

B =
• -2 1 0
• 4 3 -2
• 1 2 -1

I need to find (A + B)squared

2 + -2 0 + 1 1 + 0 is 0 1 1

and then squared is the same answer

The book has the answer as

Matrix

• 11 5 2
• 17 13 9
• 23 14 9
I know this is difficult to read but I hope you can understand it. i didn't know how to type any other way

2. $\displaystyle A+B=\begin{pmatrix}
2 & 0 & 1\\
2 & -1 & 3\\
4 & 1 & 2\end{pmatrix}+
\begin{pmatrix}
-2 & 1 & 0\\
4 & 3 & -2\\
1 & 2 & -1\end{pmatrix}=
\begin{pmatrix}
0 & 1 & 1\\
6 & 2 & 1\\
5 & 3 & 1\end{pmatrix}$

Then, $(A+B)^2=\begin{pmatrix}
11 & 5 & 2\\
17 & 13 & 9\\
23 & 14 & 9\end{pmatrix}$

3. $\left(\begin{bmatrix}
{2}\;\; {0}\;\;{1}\\
{2}\;\;{-1}\;\;{3} \\
{4}\;\;{1}\;\;{2}

\end{bmatrix} +\begin{bmatrix}
{-2}\;\; {1}\;\;{0}\\
{4}\;\;{3}\;\;{-2}\\
{1}\;\;{2}\;\;{-1}\\

\end{bmatrix}\right)^2$

$=\left(\begin{bmatrix}
{2-2\ }\;\; {\ 0+1\ }\;\;{\ 1+0}\\
{2+4\ }\;\;{\ -1+3\ }\;\;{\ 3-2}\\
{4+1\ }\;\;{\ 1+2\ }\;\;{\ 2-1}\\

\end{bmatrix}\right)^2$

$=\left(\begin{bmatrix}
{0}\;\;{1}\;\;{1}\\
{6}\;\;{2}\;\;{1}\\
{5}\;\;{3}\;\;{1}\\
\end{bmatrix}\right)^2$

$=\begin{bmatrix}
{0}\;\;{1}\;\;{1}\\
{6}\;\;{2}\;\;{1}\\
{5}\;\;{3}\;\;{1}\\
\end{bmatrix} \cdot \begin{bmatrix}
{0}\;\;{1}\;\;{1}\\
{6}\;\;{2}\;\;{1}\\
{5}\;\;{3}\;\;{1}\\
\end{bmatrix}$

$=\begin{bmatrix}
{0\cdot 0 + 1 \cdot 6 +1\cdot 5\ }\;\;{\ 0\cdot 1+1\cdot 2 + 1 \cdot 3\ }\;\;{\ 0\cdot 1+1\cdot 1 + 1\cdot 1}\\
{6\cdot 0 + 2 \cdot 6 + 1 \cdot 5\ }\;\;{\ 6\cdot 1+2\cdot 2 + 1 \cdot 3\ }\;\;{\ 6\cdot 1 +2 \cdot 1 + 1 \cdot 1}\\
{5\cdot 0+ 3 \cdot 6 + 1 \cdot 5\ }\;\;{\ 5 \cdot 1 + 3 \cdot 2 + 1 \cdot 3\ }\;\;{\ 5 \cdot 1 + 3 \cdot 1 + 1 \cdot 1}\\
\end{bmatrix}$

$=\begin{bmatrix}
{11}\;\;{5}\;\;{2}\\
{17}\;\;{13}\;\;{9}\\
{23}\;\;{14}\;\;{9}\\
\end{bmatrix}$

4. ## Thank you so very much Divideby0

I knew there was an easy explaination. I just couldn't for the life of me figure it out. Next time I am just going to come here and post because I really do not like staying up till all hours of the night.

Thank you again really!

Lori