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Stella [2.4K]
3 years ago
8

What is the solution to this equation?

Mathematics
2 answers:
____ [38]3 years ago
8 0
C is the solution x = 6
labwork [276]3 years ago
6 0
The solution to this equation is C (6)

3x - 3 = 15

3x = 15 + 3
3x = 18
3/3 x = 18/3

x = 6
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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
31 x 01111111111111111111111111
dybincka [34]
3.4444444444444444444444444444
7 0
3 years ago
Read 2 more answers
Which number property supports your answer
lys-0071 [83]
What is the question
5 0
3 years ago
Question attached as screenshot below: ONLY QUESTION 5 I have the answers to 1-4
serious [3.7K]

Given:-

x^3-6x

To graph and explain.

So the graph of the given function is,

An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function.

4 0
1 year ago
What are two equivalent ratios for 8/9
Georgia [21]
(16/18)
(24/27)

You just times 8 and 9 by the same number, like:
(8•2/9•2)=(16/18)
(8•3/9•3)=(24/27)

You could do any number:
(8•100/9•100)=(800/900)

8 0
4 years ago
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