Answer:
![A^{-1}=\left[ \begin{array}{ccc} \frac{1}{9} & \frac{4}{27} & - \frac{2}{27} \\\\ \frac{8}{9} & \frac{5}{27} & \frac{11}{27} \\\\ - \frac{4}{9} & \frac{2}{27} & - \frac{1}{27} \end{array} \right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%3D%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7D%20%5Cfrac%7B1%7D%7B9%7D%20%26%20%5Cfrac%7B4%7D%7B27%7D%20%26%20-%20%5Cfrac%7B2%7D%7B27%7D%20%5C%5C%5C%5C%20%5Cfrac%7B8%7D%7B9%7D%20%26%20%5Cfrac%7B5%7D%7B27%7D%20%26%20%5Cfrac%7B11%7D%7B27%7D%20%5C%5C%5C%5C%20-%20%5Cfrac%7B4%7D%7B9%7D%20%26%20%5Cfrac%7B2%7D%7B27%7D%20%26%20-%20%5Cfrac%7B1%7D%7B27%7D%20%5Cend%7Barray%7D%20%5Cright%5D)
Step-by-step explanation:
We want to find the inverse of ![A=\left[ \begin{array}{ccc} 1 & 0 & -2 \\\\ 4 & 1 & 3 \\\\ -4 & 2 & 3 \end{array} \right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7D%201%20%26%200%20%26%20-2%20%5C%5C%5C%5C%204%20%26%201%20%26%203%20%5C%5C%5C%5C%20-4%20%26%202%20%26%203%20%5Cend%7Barray%7D%20%5Cright%5D)
To find the inverse matrix, augment it with the identity matrix and perform row operations trying to make the identity matrix to the left. Then to the right will be inverse matrix.
So, augment the matrix with identity matrix:
![\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 4&1&3&0&1&0 \\\\ -4&2&3&0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%260%26-2%261%260%260%20%5C%5C%5C%5C%204%261%263%260%261%260%20%5C%5C%5C%5C%20-4%262%263%260%260%261%5Cend%7Barray%7D%5Cright%5D)
- Subtract row 1 multiplied by 4 from row 2
![\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ -4&2&3&0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%260%26-2%261%260%260%20%5C%5C%5C%5C%200%261%2611%26-4%261%260%20%5C%5C%5C%5C%20-4%262%263%260%260%261%5Cend%7Barray%7D%5Cright%5D)
- Add row 1 multiplied by 4 to row 3
![\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ 0&2&-5&4&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%260%26-2%261%260%260%20%5C%5C%5C%5C%200%261%2611%26-4%261%260%20%5C%5C%5C%5C%200%262%26-5%264%260%261%5Cend%7Barray%7D%5Cright%5D)
- Subtract row 2 multiplied by 2 from row 3
![\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ 0&0&-27&12&-2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%260%26-2%261%260%260%20%5C%5C%5C%5C%200%261%2611%26-4%261%260%20%5C%5C%5C%5C%200%260%26-27%2612%26-2%261%5Cend%7Barray%7D%5Cright%5D)
![\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ 0&0&1&- \frac{4}{9}&\frac{2}{27}&- \frac{1}{27}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%260%26-2%261%260%260%20%5C%5C%5C%5C%200%261%2611%26-4%261%260%20%5C%5C%5C%5C%200%260%261%26-%20%5Cfrac%7B4%7D%7B9%7D%26%5Cfrac%7B2%7D%7B27%7D%26-%20%5Cfrac%7B1%7D%7B27%7D%5Cend%7Barray%7D%5Cright%5D)
- Add row 3 multiplied by 2 to row 1
![\left[ \begin{array}{ccc|ccc}1&0&0&\frac{1}{9}&\frac{4}{27}&- \frac{2}{27} \\\\ 0&1&11&-4&1&0 \\\\ 0&0&1&- \frac{4}{9}&\frac{2}{27}&- \frac{1}{27}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%260%260%26%5Cfrac%7B1%7D%7B9%7D%26%5Cfrac%7B4%7D%7B27%7D%26-%20%5Cfrac%7B2%7D%7B27%7D%20%5C%5C%5C%5C%200%261%2611%26-4%261%260%20%5C%5C%5C%5C%200%260%261%26-%20%5Cfrac%7B4%7D%7B9%7D%26%5Cfrac%7B2%7D%7B27%7D%26-%20%5Cfrac%7B1%7D%7B27%7D%5Cend%7Barray%7D%5Cright%5D)
- Subtract row 3 multiplied by 11 from row 2
![\left[ \begin{array}{ccc|ccc}1&0&0&\frac{1}{9}&\frac{4}{27}&- \frac{2}{27} \\\\ 0&1&0&\frac{8}{9}&\frac{5}{27}&\frac{11}{27} \\\\ 0&0&1&- \frac{4}{9}&\frac{2}{27}&- \frac{1}{27}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%260%260%26%5Cfrac%7B1%7D%7B9%7D%26%5Cfrac%7B4%7D%7B27%7D%26-%20%5Cfrac%7B2%7D%7B27%7D%20%5C%5C%5C%5C%200%261%260%26%5Cfrac%7B8%7D%7B9%7D%26%5Cfrac%7B5%7D%7B27%7D%26%5Cfrac%7B11%7D%7B27%7D%20%5C%5C%5C%5C%200%260%261%26-%20%5Cfrac%7B4%7D%7B9%7D%26%5Cfrac%7B2%7D%7B27%7D%26-%20%5Cfrac%7B1%7D%7B27%7D%5Cend%7Barray%7D%5Cright%5D)
As can be seen, we have obtained the identity matrix to the left. So, we are done.
Answer:
Firstly, notice the relationship the two triangles have. They have conjoining ends that form vertical angles (looks like a middle x). Vertical angles are equivalent in measure of degrees.
Secondly, notice that the triangle on the right side is a right triangle. One of its angle's measurements are also given; 40 degrees. If you know that the sum of a triangle's angles equal 180 degrees, then simply subtract the known angles measurements from 180.
180-(90+40)= 180-130=50.
Therefore, the vertical angles measurement is equivalent to 50 degrees.
Apply the principle of the sum of all angles in a triangle equivalent to 180 degrees to the left triangle, and you will be able to find the measurement of the "?" angle.
180-(50+25)= 180-75=105
SO HERE IS YOUR ANSWER= 105 degrees is the value of the angle marked with a "?"
I hope you are having a great day too;)!
Answer: 17 -3n
Explanation:
In the given arithmetic progression 20,17,14,11,8....
first term that is a = 20
common difference that is d= a2-a1 = 17-20 = -3
let n is the nth term
= a+(n-1)d
substituting the values of first, common,difference and n
=20+(n-1) (-3)
= 20 -3n+3
=23 -3n
Since one knot is 1.15 mph.
We multiply 35 time 1.15, which equals 40.25 mph.
Then we subtract. 175 - 4.25 = 134.75
Round, and you'll get 135mph
Therefore, your answer is 135mph