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Alika [10]
3 years ago
7

Let v⃗ 1=⎡⎣⎢033⎤⎦⎥,v⃗ 2=⎡⎣⎢1−10⎤⎦⎥,v⃗ 3=⎡⎣⎢30−3⎤⎦⎥ be eigenvectors of the matrix A which correspond to the eigenvalues λ1=−1, λ2

=0, and λ3=1, respectively, and let x⃗ =⎡⎣⎢−2−40⎤⎦⎥. Express x⃗ as a linear combination of v⃗ 1, v⃗ 2, and v⃗ 3, and find Ax⃗ . x⃗ = -1 v⃗ 1+ 0 v⃗ 2+ 1 v⃗ 3. Ax⃗ = ⎡⎣⎢⎢⎢⎢⎢⎢ ⎤⎦⎥⎥⎥⎥⎥⎥
Mathematics
1 answer:
kaheart [24]3 years ago
7 0

Answer:

- x as a linear combination :

x = -1 v1+ 0 v2+ 1 v3.

- Transpose Ax = (12, -6, -6)

Step-by-step explanation:

Given v1 = (0 3 3),v2 = (1 −1 0), v3 = (3 0 −3) be eigenvectors of the matrix A which correspond to the eigenvalues λ1 = −1, λ2 = 0, and λ3 = 1, respectively, and let x = (−2 −4 0). Express x as a linear combination of v1, v2, and v3, and find Ax .

To write x as a linear combination of v1, v2, and v3

x = -1 v1+ 0 v2+ 1 v3.

To find Ax

Write A = (0 ......3 ......3 )

...................(1 ......-1 ......0)

...................(3 ......0......-3)

Since transpose x = (-2, 4, 0)

Ax =......... (0 ......3......3 )(-2)

...................(1 ......-1 ......0)(4)

...................(3 ......0......-3)(0)

= (0×-2 + 3×4 + 3×0)

...(1×-2 + -1×4 + 0×0)

.. (3×-2 + 0×4 + -3×0)

As = (12)

....(-6)

....(-6)

Transpose Ax = (12, -6, -6)

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pishuonlain [190]

we have

y=2x^{2} -8x+9


Group terms that contain the same variable, and move the constant to the opposite side of the equation

y-9=2x^{2} -8x


Factor the leading coefficient

y-9=2(x^{2} -4x)


Complete the square. Remember to balance the equation by adding the same constants to each side

y-9+8=2(x^{2} -4x+4)

y-1=2(x^{2} -4x+4)


Rewrite as perfect squares

y-1=2(x-2)^{2}

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therefore


the answer is the option C

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3 years ago
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likoan [24]

Answer:

0.0057

Step-by-step explanation:

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A web server hosting company advertises 99.999 percent guaranteed network uptime. (a) how many independent network servers would
miv72 [106K]
The solution for this problem would be:
Given that there is 99.999%.

Let denote n as the network servers and p as the reliability of each server.
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alexandr1967 [171]

Answer:

A. (-1 , 3)

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

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