**Question: **Set the following system of equations into matrix form and solve using Gauss-Jordan.

x – 2y + 4z = 9

x + y + 13z = 6

-2x + 6y – z = -10

0

**Question: **A minor league ballpark seats 8000. There are box seats that cost $10, grandstand seats that cost $5 and bleacher seats that are $3 each. When all the seats

are sold, the total revenue is $37,000. The number of bleacher seats is four times the number of box seats. How many of each type of seat are there at the

ballpark? Set up both the equations and matrix.

SET UP ONLY - DO NOT SOLVE - DON'T FORGET DOCUMENTATION

**Question: **The system of equations at right 4x + 2y - 3z = 18

-2x + 2y - z = 2

3x + 2z = 2

has been worked using the Gauss-Jordan technique to the matrix below. Get the next matrix and STOP.

1 1/2 -3/4 l 9/2

0 3 -5/2 l 11

0 -3/2 13/4 l -23/2

**Question: **Perform each of the indicated matrix operations below. If an operation is not defined, explain why it cannot be done.

(There are brackets around the the numbers below for each matrix)

a)

\(\left[ \begin{matrix}

3 & -1 & 5 \\

-2 & 4 & 6 \\

\end{matrix} \right]-\left[ \begin{matrix}

1 & -2 & 2 \\

-2 & 3 & 4 \\

\end{matrix} \right]\)

b)

\(\left[ \begin{matrix}

6 & 4 \\

2 & 5 \\

-1 & 3 \\

\end{matrix} \right]+\left[ \begin{matrix}

2 & 3 \\

2 & -2 \\

\end{matrix} \right]\)

c)

\(\left[ \begin{matrix}

2 & -3 & 4 \\

-2 & 3 & 4 \\

\end{matrix} \right]\times \left[ \begin{matrix}

-3 & 2 \\

4 & 1 \\

\end{matrix} \right]\)

d)

\[\left[ \begin{matrix}

3 & -2 & 2 \\

4 & -3 & 3 \\

\end{matrix} \right]\times \left[ \begin{matrix}

3 & -2 \\

1 & -2 \\

0 & 4 \\

\end{matrix} \right]\]

**Question: **Find the multiplicative inverse of the matrix below

\(A=\left[ \begin{matrix}

1 & 1/2 \\

2 & 3/2 \\

\end{matrix} \right]\)

**Question: **Della's Deli Shop operates at 2 locations - a big discount store and on

store this week she sold 75 ham sandwiches and 30 chicken sandwiches. On Main Street she sold 20 chicken and 35 ham sandwiches. She sold 30 steak

sandwiches on Main Street and 50 at the discount store.

a) Show the information above in a 3 X 2 matrix.

b) Della expects sales to triple for all sandwiches at both locations next week because of the ball game in town. Show the appropriate matrix operation to determine sales next week.

c) Show the matrix operation to determine sales for the two weeks combined.

**Question: **Afarmer wishes to enclose a rectangular region bordering a river with 700 feet of fencing. What is the maximum area that can be enclosed with the fencing?

**Question: **The system of equations at right 4x + 2y - 3z = 18

-2x + 2y - z = 2

3x + 2z = 2

has been worked using the Gauss-Jordan technique to the matrix below. Get the next matrix and STOP.

1 1/2 -3/4 l 9/2

0 3 -5/2 l 11

0 -3/2 13/4 l -23/2

**Question: **Perform each of the indicated matrix operations below. If an operation is not defined, explain why it cannot be done.

(There are brackets around the the numbers below for each matrix)

a)

\(\left[ \begin{matrix}

3 & -1 & 5 \\

-2 & 4 & 6 \\

\end{matrix} \right]-\left[ \begin{matrix}

1 & -2 & 2 \\

-2 & 3 & 4 \\

\end{matrix} \right]\)

b)

\(\left[ \begin{matrix}

6 & 4 \\

2 & 5 \\

-1 & 3 \\

\end{matrix} \right]+\left[ \begin{matrix}

2 & 3 \\

2 & -2 \\

\end{matrix} \right]\)

c)

\(\left[ \begin{matrix}

2 & -3 & 4 \\

-2 & 3 & 4 \\

\end{matrix} \right]\times \left[ \begin{matrix}

-3 & 2 \\

4 & 1 \\

\end{matrix} \right]\)

d)

\[\left[ \begin{matrix}

3 & -2 & 2 \\

4 & -3 & 3 \\

\end{matrix} \right]\times \left[ \begin{matrix}

3 & -2 \\

1 & -2 \\

0 & 4 \\

\end{matrix} \right]\]

**Question: **Find the multiplicative inverse of the matrix below

\(A=\left[ \begin{matrix}

1 & 1/2 \\

2 & 3/2 \\

\end{matrix} \right]\)

**Question: **Della's Deli Shop operates at 2 locations - a big discount store and on

store this week she sold 75 ham sandwiches and 30 chicken sandwiches. On Main Street she sold 20 chicken and 35 ham sandwiches. She sold 30 steak

sandwiches on Main Street and 50 at the discount store.

a) Show the information above in a 3 X 2 matrix.

b) Della expects sales to triple for all sandwiches at both locations next week because of the ball game in town. Show the appropriate matrix operation to determine sales next week.

c) Show the matrix operation to determine sales for the two weeks combined.

**Question: ** Find real numbers a, b, and c so that the span of \(\left( 1,2,1 \right)\) and \(\left( 3,2,-5 \right)\) is the subspace of \({{\mathbb{R}}^{3}}\) given by

**Question: ** Find all real numbers \({{k}_{1}},{{k}_{2}},{{k}_{3}}\) so that the function \({{k}_{1}}\log x+{{k}_{2}}\log \left( x+1 \right)+{{k}_{3}}\log \left( x+2 \right)\) is constantly zero for all positive x. You may want to differentiate first, to avoid carrying a lot of logarithms around in your calculations.

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