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3 years ago

Standard from of linear equation

Mathematics

1 answer:

Mashcka [7]3 years ago

4 0

# of bb's = (350-30*4)/22
f(x) = (230/22) = 10.45

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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

3 years ago

2xsquared is the same as what?

Rus_ich [418]

Answer:

$2x^2=2xx$

6 0

3 years ago

What is the median?<br> -2 -3 8 -6 -9

mars1129 [50]

Answer:

-3

Step-by-step explanation:

its the middle number so you put them in order and get the ndeswer just whatevers in the midde

-9 -6 -3 -2 8

8 0

3 years ago

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laura bought a square canvas to paint a picture of her cat. one side measures 22 centimeters. what is the area of canvas.

soldier1979 [14.2K]

If we know that Laura's canvas is square, and one side is 22cm,

area of a square is l*w, with a special case of l=w

the area will be
A= l*w=22*22=484cm^2

also, Asquare is=l^2

4 0

3 years ago

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Asir borrowed money from his parents to purchase a video gaming system for $473.89(including tax). About how much are his monthl

stepladder [879]

Answer:

Step-by-step explanation:

473.89/12= $39.49083 or $39.50 a month

6 0

2 years ago