Consider the operation is 
.
Given:
The augmented matrix below represents a system of equations.
![\left[\left.\begin{matrix}1&0&1\\1&3&-1\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-9\\-2\end{matrix}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cleft.%5Cbegin%7Bmatrix%7D1%260%261%5C%5C1%263%26-1%5C%5C3%262%260%5Cend%7Bmatrix%7D%5Cright%7C%5Cbegin%7Bmatrix%7D-1%5C%5C-9%5C%5C-2%5Cend%7Bmatrix%7D%5Cright%5D)
To find:
Matrix results from the operation .
Step-by-step explanation:
We have,
After applying , we get
![\left[\left.\begin{matrix}1&0&1\\-3(1)&-3(3)&-3(-1)\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-3(-9)\\-2\end{matrix}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cleft.%5Cbegin%7Bmatrix%7D1%260%261%5C%5C-3%281%29%26-3%283%29%26-3%28-1%29%5C%5C3%262%260%5Cend%7Bmatrix%7D%5Cright%7C%5Cbegin%7Bmatrix%7D-1%5C%5C-3%28-9%29%5C%5C-2%5Cend%7Bmatrix%7D%5Cright%5D)
![\left[\left.\begin{matrix}1&0&1\\-3&-9&3\\3&2&0\end{matrix}\right|\begin{matrix}-1\\27\\-2\end{matrix}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cleft.%5Cbegin%7Bmatrix%7D1%260%261%5C%5C-3%26-9%263%5C%5C3%262%260%5Cend%7Bmatrix%7D%5Cright%7C%5Cbegin%7Bmatrix%7D-1%5C%5C27%5C%5C-2%5Cend%7Bmatrix%7D%5Cright%5D)
Therefore, the correct option is A.
Answer:
32w + 24v - 48
Step-by-step explanation:
- 8(- 4w - 3v + 6) ← multiply each term in the parenthesis by - 8
= 32w + 24v - 48
Let's come up with an equation for the numbers. We know that there are 136 faculty members, and there are 6 professors for every 11 lecturers. The equation could look something like this:
(6 * x) + (11 * x) = 136.
First, combine like terms:
6x + 11x = 136
17x = 136
Now, divide both sides by 17.
17x/17 = 136/17
x = 8.
Now, to check, plug in 8 for x in our equation:
(6 * 8) + (11 * 8) = 136
48 + (11 * 8) = 136
48 + 88 = 136
So to answer the question, they have 48 professors! :)
Answer:
n-1
Step-by-step explanation:
Consecutive means that they have a difference of one, so the expression will be n-1.
Answer:
1 cm = 3 feet.
Step-by-step explanation:
Divide 15 by 5 to get 3; on the blueprint, every centimeter represents 3 feet.
