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:
12^0=1
Step-by-step explanation:
anything to the power of 0 is equal to 1
Area is multiplying the width and the length so
area= 3.2 × 1.5 = 4.8
and perimeter is adding all sides together so
perimeter= 3.2 + 3.2 + 1.5 + 1.5 = 9.4
