Let's use Gaussian elimination. Consider the augmented matrix,
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\-1 & 2 & 3 & 0 & 1 & 0\\1 & 1 & 4 & 0 & 0 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C-1%20%26%202%20%26%203%20%26%200%20%26%201%20%26%200%5C%5C1%20%26%201%20%26%204%20%26%200%20%26%200%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add row 1 to row 2, and add -1 (row 1) to row 3:
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 2 & 5 & -1 & 0 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C0%20%26%201%20%26%202%20%26%201%20%26%201%20%26%200%5C%5C0%20%26%202%20%26%205%20%26%20-1%20%26%200%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add -2 (row 2) to row 3:
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C0%20%26%201%20%26%202%20%26%201%20%26%201%20%26%200%5C%5C0%20%26%200%20%26%201%20%26%20-3%20%26%20-2%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add -2 (row 3) to row 2:
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C0%20%26%201%20%26%200%20%26%207%20%26%205%20%26%20-2%5C%5C0%20%26%200%20%26%201%20%26%20-3%20%26%20-2%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add row 2 and row 3 to row 1:
![\left[\begin{array}{ccc|ccc}1 & 0 & 0 & 5 & 3 & -1\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%200%20%26%200%20%26%205%20%26%203%20%26%20-1%5C%5C0%20%26%201%20%26%200%20%26%207%20%26%205%20%26%20-2%5C%5C0%20%26%200%20%26%201%20%26%20-3%20%26%20-2%20%26%201%5Cend%7Barray%7D%5Cright%5D)
So the inverse is

Step-by-step explanation:
I think chocolate fairness criterion has been violated because under the unknown voting method the winner was chocolate but upon calling the store they ordered for yellow cake not chocolate
Answer:
Step-by-step explanation:
length = 120/8 = 15 feet
perimeter = (15 + 8) x 2 = 46 feet
The best way to answer this would be making a graph
For 1 sign it costs 54.50 and he makes 15
For 2 signs it costs 59 and he makes 30
For 3 signs it costs 63.50 and he makes 45
For 4 signs it costs 68 and he makes 60
For 5 signs it costs 72.50 and he makes 75
This means that after 5 signs Larry will be making profit