Answer:
The triangle is a right triangle
Step-by-step explanation:
For the triangle to be right, Pythagoras’ theorem must be obeyed
According to the theorem, the square of the longest side (the hypotenuse) equals the sum of the squares of the two other sides
Now, from the given side lengths, the highest value is 10;
squaring this, we have 10^2 = 100
Squaring and adding the other values, we have
6^2 + 8^2 = 36 + 64 = 100
This mean the values are equal and the Pythagoras’ theorem is obeyed
Hence, we can conclude that the triangle with the given side lengths is a right triangle
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
Answer:
872.52
Step-by-step explanation:
Answer:
(-11, -12)
Step-by-step explanation:
we need one variable to x out
on the note of x, lets cancel out the xs
6x+3y=-102
3x+y=-45 < same as 6x+2y-90
6x+3y=-102
-
6x+2y=-90
y=-12
substitute y in
3x-12=-45
3x=-33
x=-11
(-11, -12)
Please give brainliest :)
