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mario62 [17]
3 years ago
14

Help!! I'm really confused, please explain how you got it

Mathematics
1 answer:
olasank [31]3 years ago
3 0
3a²-4b
3(-6)²-4(-5)
108+20
128
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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
What is the value of x?
mariarad [96]
X by itself is 1, otherwise it is the number to the left
4 0
4 years ago
Read 2 more answers
BRAINLIEST ASAP! PLEASE HELP ME :)
Nitella [24]

The answer is [ ∠A ≅ ∠A; A F/AB = AG/AC = 3 ]

Both triangles are the same just different sizes.

The length of A F is 9 units. The length of AB is 3 units.

To find the scale factor, just divide.

9 / 3 = 3

The length of AG is 6 units. The length of AC is 2 units.

To find the scale factor, just divide.

6 / 2 = 3

The only logical answer is B because the ratio's are written to where when you solve them, you get the scale factor 3.

Best of Luck!

6 0
3 years ago
Is 226.08cm to the third power the correct response?
drek231 [11]
Surface Area of a cylinder 2(π•r²)+(2π•r)•h

So

If the diameter is 8 then the radius is 4. the height is 5.

so you have, 2(3.14•4²)+(2•3.14•4)•5

solve. PEMDAS
Parentheses & Exponents first.
2(3.14•16)+(2•3.14•4)•5
2(50.24)+(6.28•4)•5
2(50.24)+(25.12)•5
Multiplication & Division second (left to right)
100.48+125.6
Add & Subtract (left to right)
226.08cm

5 0
3 years ago
One and a half x + 3/4 x equals 5/8
USPshnik [31]
1 and 1/2x+3/4x=5/8
combine x's
1 and 1/2x=4/4x+2/4x=6/4x
6/4x+3/4x=5/8=9/4x
9/4x=5/8
multiply both sides by 8
18x=5
x=5/18

x=5/18 or aprox 0.277777777777

5 0
4 years ago
Read 2 more answers
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