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professor190 [17]

4 years ago

5

Dale is trying to find the height of a triangular wall.

2 answers:

Gnom [1K]4 years ago

6 0

Yes good luck dale.
you have a measuring tape? that might help a little bit

Tju [1.3M]4 years ago

4 0

We certainly wish him all the best, and caution him to be careful.

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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

How do you do question b?

notsponge [240]

Part (b)

We use the result of part (a) and plug in (x,y) = (0,0). This is directly from the initial condition y(0) = 0.

$\arcsin(4y) = x^2 + C\\\\\arcsin(4*0) = (0)^2 + C\\\\\arcsin(0) = C\\\\0 = C\\\\C = 0\\\\$

-----------------

This means,

$\arcsin(4y) = x^2 + C\\\\\arcsin(4y) = x^2 + 0\\\\\arcsin(4y) = x^2\\\\4y = \sin(x^2)\\\\y = \frac{1}{4}\sin(x^2)\\\\$

is the solution with the initial condition y(0) = 0.

6 0

3 years ago

44/35 as a mixed number

joja [24]

44/35 = 1 9/35

So, your answer is 1 9/35

4 0

3 years ago

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Which figure has the largest shaded region?

lions [1.4K]

Answer:

is A

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Pic attached for further detail

marissa [1.9K]

I dont get what you asking

8 0

3 years ago