10.1 Homework: introduction to matrices

In the following matrix…

$\left[\begin{array}{cccccc}1& 3& 7& 4& 9& 3\\ 6& 3& 7& 0& 8& 1\\ 8& 5& 0& 7& 3& 2\\ 8& 9& 5& 4& 3& 0\\ 6& 7& 4& 2& 9& 1\end{array}\right]$

• A

  What are the dimensions? __ $\times$ __

• B

  Copy the second column here:

• C

  Copy the third row here:

• D

  Write another matrix which is equal to this matrix.

Add the following two matrices.

$\left[\begin{array}{ccc}2& 6& 4\\ 9& n& 8\end{array}\right]+\left[\begin{array}{ccc}5& 7& 1\\ 9& \mathrm{-n}& 3n\end{array}\right]=$

Add the following two matrices.

$\left[\begin{array}{ccc}2& 6& 4\\ 9& n& 8\end{array}\right]+\left[\begin{array}{cc}5& 7\\ 9& \mathrm{-n}\end{array}\right]=$

Subtract the following two matrices.

$\left[\begin{array}{ccc}2& 6& 4\\ 9& n& 8\end{array}\right]-\left[\begin{array}{ccc}5& 7& 1\\ 9& \mathrm{-n}& 3n\end{array}\right]=$

Solve the following equation for $x$ and $y$ . (That is, find what $x$ and $y$ must be for this equation to be true.)

$\left[\begin{array}{c}2x\\ 5y\end{array}\right]+\left[\begin{array}{c}x+y\\ -6x\end{array}\right]=\left[\begin{array}{c}6\\ 2\end{array}\right]$

Solve the following equation for $x$ and $y$ . (That is, find what $x$ and $y$ must be for this equation to be true.)

$\left[\begin{array}{c}x+y\\ \mathrm{3x}-\mathrm{2y}\end{array}\right]+\left[\begin{array}{c}\mathrm{4x}-y\\ x+\mathrm{5y}\end{array}\right]=\left[\begin{array}{cc}3& 5\\ 7& 9\end{array}\right]$