91Ó°ÊÓ

For exercises 26 and 27, use the advertisement shown at the right.

What are the dimensions of the matrix?

Use Cramer’s Rule to solve each system of equations.

$a-2b+c=7$

$6a+2b-2c=4$

$4a+6b+4c=14$

Use matrices$A$, $B$, $C$and $D$to find the following.

$A=\left[\begin{array}{cc}5& 7\\ −1& 6\\ 3& −9\end{array}\right],\text{ â¶Ä‰}B=\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right],\text{ â¶Ä‰}C=\left[\begin{array}{cc}0& 4\\ −2& 5\\ 7& −1\end{array}\right],\text{ â¶Ä‰}D=\left[\begin{array}{cc}6& 2\\ 9& 0\\ −3& 0\end{array}\right]$

27. $6B-2A$

Use$A=\left[\begin{array}{cc}1& −2\\ 4& 3\end{array}\right]$,$B=\left[\begin{array}{cc}−5& 2\\ 4& 3\end{array}\right]$, and $C=\left[\begin{array}{cc}5& 1\\ 2& −4\end{array}\right]$ and scalar $c=3$to determine whether the equation is true for the given matrices.

$AC+BC=(A+B)C$

Find the inverse of each matrix, if it exists.27.

$\left[\begin{array}{cc}−2& 0\\ 5& 6\end{array}\right]$

For exercises 26-28, use quadrilateral $QRST$ shown at the right.

27. Graph the pre-image and the image.

Use$A=\left[\begin{array}{cc}1& −2\\ 4& 3\end{array}\right]$,$B=\left[\begin{array}{cc}−5& 2\\ 4& 3\end{array}\right]$, and $C=\left[\begin{array}{cc}5& 1\\ 2& −4\end{array}\right]$ and scalar $c=3$to determine whether the equation is true for the given matrices.

$c\left(AB\right)=A\left(cB\right)$

Evaluate each determinant using expansion by minors.

$\left|\begin{array}{ccc}7& 3& −4\\ −2& 9& 6\\ 0& 0& 0\end{array}\right|$

Use matrices$A$, $B$, $C$and $D$to find the following.

$A=\left[\begin{array}{cc}5& 7\\ −1& 6\\ 3& −9\end{array}\right],\text{ â¶Ä‰}B=\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right],\text{ â¶Ä‰}C=\left[\begin{array}{cc}0& 4\\ −2& 5\\ 7& −1\end{array}\right],\text{ â¶Ä‰}D=\left[\begin{array}{cc}6& 2\\ 9& 0\\ −3& 0\end{array}\right]$

28. $3C-4A+B$

Use Cramer’s Rule to solve each system of equations.

$r-2s-5t=-1$

$r+2s-2t=5$

$4r+s+t=-1$