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3 years ago

7

Please answer this question now in two minutes

1 answer:

KonstantinChe [14]3 years ago

5 0

Answer:

c. Not enough information

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Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are

alexgriva [62]

Answer:

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

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

4 years ago

coach cliffman made a deposit of $1,800 into an account that earns 2% annual simple interest. find the amount of interest that c

igomit [66]

He earns $36 after 3 years

3 0

3 years ago

Let f(x) = 1/x. Find a number b so that the average rate of change of f on the interval

Bezzdna [24]

Answer:

huh try multiplying

Step-by-step explanation:

6 0

4 years ago

There are blue, red and green pencils in the box—20 pencils total. There are 6 times more green pencils than blue pencils. There

lana [24]

Answer:

You have to take 15 pens to get at least one red pencil.

Step-by-step explanation:

If there were one red and 6 green pens, there would be more red than green pens.

If there were 3 or more blue and thus 18 or more green pens, the number of pens would be over 20.

So there must be 2 blue, 12 green and thus 6 red pencils. So you have to take at least 15 pens to be sure that you got a red one.

5 0

3 years ago

What is the midpoint of the segment shown below?

Bogdan [553]

C. 5/2, 3 this is the answer

3 0

3 years ago

Read 2 more answers