Answer:
Step-by-step explanation:
Absolute value inside the brackets will always be positive*
1. 7
2.15
3.0
4. -5
5.-3
6.3
7.17
8.5
9.-101
10.0
11.16
12.1
Hope this helped!
Answer - x= 4.75
explanation
Hello, let's note A the matrix, we need to find
such that A
=
I, where I is the identity matrix, so the determinant is 0, giving us the characteristic equation as

We just need to solve this equation using the discriminant.

And then the eigenvalues are.

To find the basis, we have to solve the system of equations.
![A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}](https://tex.z-dn.net/?f=A%5Clambda_1-%5Clambda_1%20I%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3i%263%5C%5C-3%263i%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%3D3%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Di%261%5C%5C-1%26i%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5Ctext%7BFor%20a%20vector%20%28a%2Cb%29%2C%20we%20need%20to%20find%20a%20and%20b%20such%20that.%7D%5C%5C%5C%5C%5Cbegin%7Bcases%7Dai%2Bb%3D0%5C%5C-a%2Bbi%3D0%5Cend%7Bcases%7D%5C%5C%5C%5C%5Ctext%7B%281%2C-i%29%20is%20a%20base%20of%20this%20space%2C%20as%20i-i%3D0%20and%20-1-%7Di%5E2%5Ctext%7B%3D-1%2B1%3D0.%7D)
![A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}](https://tex.z-dn.net/?f=A%5Clambda_2-%5Clambda_2%20I%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-3i%263%5C%5C-3%26-3i%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%3D3%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-i%261%5C%5C-1%26-i%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Ctext%7BFor%20a%20vector%20%28a%2Cb%29%2C%20we%20need%20to%20find%20a%20and%20b%20such%20that.%7D%5C%5C%5C%5C%5Cbegin%7Bcases%7D-ai%2Bb%3D0%5C%5C-a-bi%3D0%5Cend%7Bcases%7D%5C%5C%5C%5C%5Ctext%7B%281%2Ci%29%20is%20a%20base%20of%20this%20space%20as%20-i%2Bi%3D0%20and%20-1-i%2Ai%3D0.%7D)
Thank you
Answer:
160in i believe
Step-by-step explanation:
sorry im probably wrong lol