$P=\left(\begin{array}{ccc}-\frac{2}{3}&-\frac{2}{3}&\frac{1}{3}\\\frac{1}{\sqrt{5}}&0&\frac{2}{\sqrt{5}}\\-\frac{4}{3\sqrt{5}}&\frac{\sqrt{5}}{3}&\frac{2}{3\sqrt{5}}\end{array}\right)$

Step-by-step explanation:

It is a result that a matrix $A$ is orthogonally diagonalizable if and only if $A$ is a symmetric matrix. According with the data you provided the matrix should be

$A=\left(\begin{array}{ccc}-9&-4&2\\ -4&-9&2\\2&2&-6\\\end{array}\right)$

We know that its eigenvalues are $\lambda_{1}=-14, \lambda_{2}=-5$ , where $\lambda_{2}=-5$ has multiplicity two.

So if we calculate the corresponding eigenspaces for each eigenvalue we have

$E_{\lambda_{1}=-14}=\langle(-2,-2,1)\rangle$ , $E_{\lambda_{2}=-5}=\langle(1,0,2),(-1,1,0)\rangle.$ .

With this in mind we can form the matrices $P, D$ that diagonalizes the matrix $A$ so.

$P=\left(\begin{array}{ccc}-2&-2&1\\1&0&2\\-1&1&0\\\end{array}\right)$

and

$D=\left(\begin{array}{ccc}-14&0&0\\0&-5&0\\0&0&-5\\\end{array}\right)$

Observe that the rows of $P$ are the eigenvectors corresponding to the eigen values.

Now you only need to normalize each row of $P$ dividing by its norm, as a row vector.

The matrix you have to obtain is the matrix shown below

3 0

3 years ago

What is 20% of $80.00?

iren [92.7K]

20% of (US$ 80) =16 US$

8 0

3 years ago

Read 2 more answers

$16 is to 116.1 as what amount is to 178.4 ?

Nat2105 [25]

The answer would be $78..

3 0

3 years ago

PLEASE ANSWER + BRAINLIEST!!!!

astra-53 [7]

Answer:

Y= 3.2b + 100

Step-by-step explanation:

That is the equation needed to find the value of b. since Omar bought the cup at the fixed price of 100 we know that no matter what the answer has to be over 100. So that becomes our Y intercept. 3.2 percent is how much the price inflates every year.

8 0

2 years ago