Question 1

Can non-square matrices have inverses? Why or why not?

Accepted Answer

The answer of Can non-square matrices have inverses? Why or...

Question 2

Is this a square matrix? Why or why not?

Accepted Answer

The answer of Is this a square matrix? Why or...

Question 3

Describe the proper form for the system to be in before the Gauss-Jordan method can be  used.

Accepted Answer

The answer of Describe the proper form for the system...

Question 4

Solve the system of equations by using the inverse of the coefficient matrix.
-$
\begin{array}{l}
4 x+8 y-z=45 \
x+5 y+7 z=99 \
-7 x+y+z=-19
\end{array}
$

Accepted Answer

A)  $ (5,9,7) $ 
B)  $ (6,7,7) $ 
C)  $ (5,-9,-7) $ 
D)  $ (9,7,9) $

Question 5

Solve the problem.
-A simplified economy has only two industries, the electric company and the gas company. Each dollar's worth of the electric company's output requires 0.20 of its own output and 0.4 of the gas Company's output. Each dollar's worth of the gas  company's output requires 0.50 of its own output And 0.7 of the electric company's output. What should the production of electricity and gas be (in Dollars)if there is a $16 million demand for electricity and a $7 million demand for gas?

Accepted Answer

A) Electricity: $107.5 million; gas: $100 million 
B) Electricity: $115 million; gas: $103.5 million 
C) Electricity: $125 million; gas: $92.5 million 
D) Electricity: $97.5 million; gas: $103 million

Question 6

Find the matrix product, if possible.
-$$
\left[\begin{array}{rr}
-1 & 3 \
5 & 4
\end{array}\right]\left[\begin{array}{lll}
0 & -2 & 4 \
1 & -3 & 2
\end{array}\right]
$$

Accepted Answer

A)  $ \left[\begin{array}{rrr}3 & -7 & 2 \ 4 & -22 & 28\end{array}\right] $ 
B)  $ \left[\begin{array}{rrr}3 & 4 & -7 \ -22 & 2 & 28\end{array}\right] $ 
C)  $ \left[\begin{array}{rr}0 & -6 \ 12 & 5 \ -12 & 8\end{array}\right] $ 
D)  Does not exist

Question 7

Solve the system of equations by using the inverse of the coefficient matrix.
-$
\begin{array}{rr}
x-2 y+3 z & =3 \
y-z+w & =-6 \
-2 x+2 y-2 z+4 w & =-18 \
2 y-3 z+w & =-10
\end{array}
$

Accepted Answer

A)  $ (-2,3,3,-6) $ 
B)  $ (-2,2,3,-5) $ 
C)  $ (-3,2,4,-5) $ 
D)  $ (-1,1,2,-4) $

Question 8

Solve the problem.
-A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers R and S. What is The cost of 100 batches of each candy using ingredients from supplier S?

Accepted Answer

A)  $ \$ 16,500 $ 
B)  $ \$ 6600 $ 
C)  $ \$ 13,200 $ 
D)  $ \$ 12,000 $

Question 9

Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the
inverse doesn't exist.
-$$
\begin{array}{l}
-3 x+9 y=9 \
3 x+2 y=13
\end{array}
$$

Accepted Answer

A)  $ (3,2) $ 
B)  $ (-3,-2) $ 
C)  $ (-2,-3) $ 
D)  $ (2,3) $

Question 10

Use a graphing calculator to find the matrix product and/or sum.
-$$
\mathrm{A}=\left[\begin{array}{rrrr}
11 & 14 & 18 & 18 \
30 & 5 & 7 & 2 \
11 & 3 & 2 & 1 \
5 & 32 & 5 & 19
\end{array}\right] \mathrm{B}=\left[\begin{array}{rrr}
12 & 5 & 3 \
18 & 8 & 12 \
7 & 4 & 2 \
21 & 15 & 0
\end{array}\right]
$$

Accepted Answer

A)  $ \left[\begin{array}{rrr}888 & 509 & 237 \ 541 & 248 & 164 \ 221 & 102 & 73 \ 1070 & 586 & 409\end{array}\right] $ 
B)  $ \left[\begin{array}{rrr}732 & 305 & 113 \ 792 & 352 & 528 \ 119 & 68 & 34 \ 1281 & 915 & 0\end{array}\right] $ 
C) 
$ \left[\begin{array}{rrrr}220 & 280 & 360 & 360 \ 1140 & 190 & 266 & 76 \ 143 & 39 & 26 & 13 \ 180 & 1152 & 180 & 684\end{array}\right] $ 
D)  Does not exist

Exam 2: Systems of Linear Equations and Matrices

Can non-square matrices have inverses? Why or why not?

Is this a square matrix? Why or why not?

Describe the proper form for the system to be in before the Gauss-Jordan method can be used.

Solve the system of equations by using the inverse of the coefficient matrix. - $\begin{array}{l}4 x+8 y-z=45 \\x+5 y+7 z=99 \\-7 x+y+z=-19\end{array}$

Find the matrix product, if possible. - $\left[\begin{array}{rr}-1 & 3 \\5 & 4\end{array}\right]\left[\begin{array}{lll}0 & -2 & 4 \\1 & -3 & 2\end{array}\right]$

Solve the system of equations by using the inverse of the coefficient matrix. - $\begin{array}{rr}x-2 y+3 z & =3 \\y-z+w & =-6 \\-2 x+2 y-2 z+4 w & =-18 \\2 y-3 z+w & =-10\end{array}$

Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the inverse doesn't exist. - $\begin{array}{l}-3 x+9 y=9 \\3 x+2 y=13\end{array}$

Use a graphing calculator to find the matrix product and/or sum. - $\mathrm{A}=\left[\begin{array}{rrrr}11 & 14 & 18 & 18 \\30 & 5 & 7 & 2 \\11 & 3 & 2 & 1 \\5 & 32 & 5 & 19\end{array}\right] \mathrm{B}=\left[\begin{array}{rrr}12 & 5 & 3 \\18 & 8 & 12 \\7 & 4 & 2 \\21 & 15 & 0\end{array}\right]$

Exam 2: Systems of Linear Equations and Matrices

Can non-square matrices have inverses? Why or why not?

Is this a square matrix? Why or why not?

Describe the proper form for the system to be in before the Gauss-Jordan method can be used.

Solve the system of equations by using the inverse of the coefficient matrix. - 4x+8y−z=45x+5y+7z=99−7x+y+z=−19\begin{array}{l}4 x+8 y-z=45 \\x+5 y+7 z=99 \\-7 x+y+z=-19\end{array}4x+8y−z=45x+5y+7z=99−7x+y+z=−19​

Find the matrix product, if possible. - [−1354][0−241−32]\left[\begin{array}{rr}-1 & 3 \\5 & 4\end{array}\right]\left[\begin{array}{lll}0 & -2 & 4 \\1 & -3 & 2\end{array}\right][−15​34​][01​−2−3​42​]

Solve the problem. -A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers R and S. What is The cost of 100 batches of each candy using ingredients from supplier S?

Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the inverse doesn't exist. - −3x+9y=93x+2y=13\begin{array}{l}-3 x+9 y=9 \\3 x+2 y=13\end{array}−3x+9y=93x+2y=13​

Solve the system of equations by using the inverse of the coefficient matrix. - $\begin{array}{l}4 x+8 y-z=45 \\x+5 y+7 z=99 \\-7 x+y+z=-19\end{array}$

Find the matrix product, if possible. - $\left[\begin{array}{rr}-1 & 3 \\5 & 4\end{array}\right]\left[\begin{array}{lll}0 & -2 & 4 \\1 & -3 & 2\end{array}\right]$

Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the inverse doesn't exist. - $\begin{array}{l}-3 x+9 y=9 \\3 x+2 y=13\end{array}$