12.4.a. Computing diagonalizations 1
0.0/10.0 points (graded)
The matrix $A$ given below has eigenvalues $\lambda_1 = -3$, $\lambda_2 = 0$. Diagonalize this matrix, i.e. find an invertible matrix $P$ and a diagonal matrix $D$ such that $A = PDP^{-1}$.
$A = \begin{bmatrix} 3 & 0 & 6\\ 6 & -3 & 6\\ -3 & 0 & -6 \end{bmatrix}$
How to enter matrices.
Matrices should be entered row by row, enclosing each row in square brackets. There must be additional square brackets at the beginning and at the end of the whole matrix. For example, if you want to enter the matrix
$\begin{bmatrix} 2 & -\frac{3}{2} & 4\\ 0 & \frac{1}{2} & 2 \end{bmatrix}$
then you should do it as follows:
[[2, -3/2, 4], [0, 1/2, 2]]
Do not forget about commas between matrix entries and between rows.
Enter the matrix $P$:
[[0,2/3,-2/3],[1,2/3,-13/33],[0,-1/3,2/3]]