Answer:
x=-7, y=2
Step-by-step explanation:
You are given the matrix equation
![\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right] \cdot \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-18\\13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-2%5C%5C-1%263%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-18%5C%5C13%5Cend%7Barray%7D%5Cright%5D)
Find the inverse matrix for the matrix
![\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-2%5C%5C-1%263%5Cend%7Barray%7D%5Cright%5D)
1. The determinant is
![\left|\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right]\right|=2\cdot 3-(-1)\cdot (-2)=6-2=4](https://tex.z-dn.net/?f=%5Cleft%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-2%5C%5C-1%263%5Cend%7Barray%7D%5Cright%5D%5Cright%7C%3D2%5Ccdot%203-%28-1%29%5Ccdot%20%28-2%29%3D6-2%3D4)
2.
3. Inverse matrix is
![\dfrac{1}{4}\left[\begin{array}{cc}3&1\\2&2\end{array}\right]^T=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%261%5C%5C2%262%5Cend%7Barray%7D%5Cright%5D%5ET%3D%5Cdfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%262%5C%5C1%262%5Cend%7Barray%7D%5Cright%5D)
So, the solution of the equation is
![\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right]\cdot \left[\begin{array}{c}-18\\13\end{array}\right]=\\ \\=\dfrac{1}{4}\left[\begin{array}{cc}3\cdot(-18)+2\cdot 13\\1\cdot (-18)+2\cdot 13\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{c}-28\\8\end{array}\right]=\left[\begin{array}{c}-7\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cdfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%262%5C%5C1%262%5Cend%7Barray%7D%5Cright%5D%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-18%5C%5C13%5Cend%7Barray%7D%5Cright%5D%3D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%5Ccdot%28-18%29%2B2%5Ccdot%2013%5C%5C1%5Ccdot%20%28-18%29%2B2%5Ccdot%2013%5Cend%7Barray%7D%5Cright%5D%3D%5Cdfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-28%5C%5C8%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-7%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
You have to sit calmly and quietly and look over this one for a few minutes,
until you see what's going on.
When the top triangle got flopped over to make the bottom one,
the 12-cm side on top made another 12-cm side on the bottom.
Also, the short 6-cm piece made another 6-cm piece hooked onto it,
and when those are put together, they make 12-cm all together.
So now, look at the whole outside triangle that you have, after the two
inside ones are put together. The top slanty side is 12-cm, the bottom
slanty side is 12-cm, and the straight up-and-down side is also 12-cm.
The new big triangle is an equilateral triangle !
What do you know about an equilateral triangle ?
-- All three sides are the same length.
-- All three angles are the same size.
If all three angles are the same size, how big is each one ?
Hint: The three angles of <em>every</em> triangle add up to 180 degrees.
So angle-y must be 1/3 of 180 = 60 degrees.
Answer:
Error in the third line.
Step-by-step explanation:
There is an error in the third line.
We are dividing through by 7 but mx is not divided by 7.
Correct solution is:
mx + 7nx =7
x(m + 7n) = 7
x = 7 / (m + 7n).
Since a slope differe, this is not linear relationship. Simply, if you connect all points on the graph, they will not lie on the same line. Two next graphs represent the linear relationships, so they represent the linear relationship.
