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Mathematics

1 answer:

katen-ka-za [31]3 years ago

8 0

<h2>Answer:</h2>

The last answer - 9x squared y squared

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The matrix A = −14 −6 6 28 12 −4 0 0 4 has characteristic polynomial

rosijanka [135]

Answer:

Characteristic equation:

$p(\lambda) = -\lambda^3 + 2\lambda^2 + 8\lambda$

Eigen values:

$\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4$

Step-by-step explanation:

We are given the matrix:

$\displaystyle\left[\begin{array}{ccc}-14&-6&6\\28&12&-4\\0&0&4\end{array}\right]$

The characteristic equation can be calculated as:

$det(A-\lambda I) = 0\\|A-\lambda I| = 0$

We follow the following steps to calculate characteristic equation:

$=det\Bigg(\displaystyle\left[\begin{array}{ccc}-14&-6&6\\28&12&-4\\0&0&4\end{array}\right]-\lambda\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\Bigg)\\\\= det\Bigg(\displaystyle\left[\begin{array}{ccc}-14-\lambda&-6&6\\28&12-\lambda&-4\\0&0&4-\lambda\end{array}\right]\Bigg)\\\\=(-14-\lambda)[(12-\lambda)(4-\lambda)]+6[28(4-\lambda)]-6[(28)(0)-(12-\lambda)(0)]\\\\= -\lambda^3 + 2\lambda^2 + 8\lambda$

$p(\lambda)= -\lambda^3 + 2\lambda^2 + 8\lambda$

To obtain the eigen values, we equate the characteristic equation to 0:

$p(\lambda) = -\lambda^3 + 2\lambda^2 + 8\lambda = 0\\-\lambda(\lambda^2-2\lambda-8) = 0\\-\lambda(\lambda^2-4\lambda+2\lambda-8) = 0\\-\lambda[(\lambda(\lambda-4)+2(\lambda-4)] = 0\\-\lambda(\lambda+2)(\lambda-4) = 0 \\\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4$

We can arrange the eigen values as:

$\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4\\-2 < 0 < 4\\\lambda_2 < \lambda_1 < \lambda_3$

3 0

3 years ago

Brian wants to have $7000 in the bank in 10 years. He deposits $3000 today at 8% interest compounded semiannually,After keeping

AveGali [126]

Total = Principal * ((1 + rate/n)^(n*years)
Total = 3,000 * (1.04)^20
Total = 3,000 *<span> <span> <span> 2.191123143 </span> = </span></span> <span> <span> <span> 6,573.37</span></span></span>
So, he will have to add (7,000 - <span>6,573.37) =
$ 426.63
answer is b
Here's a calculator to check your work http://www.1728.org/compint.htm
</span>

6 0

4 years ago

Read 2 more answers

What expressions are equivalent to 5x + (x+6) + 3x

anyanavicka [17]

Answer:

9x + 6

Step-by-step explanation:

<u>Step 1: Distribute</u>

5x + (x + 6) + 3x

5x + x + 6 + 3x

<u>Step 2: Combine like terms</u>