You find the eigenvalues of a matrix A by following these steps:
- Compute the matrix
, where I is the identity matrix (1s on the diagonal, 0s elsewhere) - Compute the determinant of A'
- Set the determinant of A' equal to zero and solve for lambda.
So, in this case, we have
![A = \left[\begin{array}{cc}1&-2\\-2&0\end{array}\right] \implies A'=\left[\begin{array}{cc}1&-2\\-2&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right]=\left[\begin{array}{cc}1-\lambda&-2\\-2&-\lambda\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D%20%5Cimplies%20A%27%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Clambda%260%5C%5C0%26%5Clambda%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1-%5Clambda%26-2%5C%5C-2%26-%5Clambda%5Cend%7Barray%7D%5Cright%5D)
The determinant of this matrix is
Finally, we have
So, the two eigenvalues are
<span>If you know 2 sides and an included angle, the area formula is:
</span>
<span>Area = ½ • side 1 • sine (A) • side 2
</span>
<span>Area = ½ • 2 * sine (60) * sq root (2)
</span>
<span>Area =sine (60) * sq root (2)
</span>
<span>The sine of 60 degrees = sq root (3) / 2
</span>
Area = sq root (6) / 2
15/18 - 2/18 = 13/18
Find the least common multiple of 6 and 9. The LCM is 18. In order to get 18 on the denominator with 6, you have to multiply by 3 because 6 times 3 is 18. You have to multiply 3 to the numerator, so 5 times 3 is 15. Thus, the first fraction is 15/18. To get the second, you need to find what would get you 18 on the denominator with 9. You need 2, so 9 times 2 is 18. You have to multiply 2 to the numerator, so 1 times 2 is 2. Thus, the second fraction is 2/18.
Step-by-step explanation:
- 4x-(x+7)=2(x+3)
- 4x-x-7=2x+6
- 3x-2x=6+7
- x=13
hope it helps.
It moves the graph to the right "5" units
And down 3 units
