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Mathematics

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love history [14]3 years ago

6 0

Yes, Brainly is a very useful app. I love helping people, and it allows me to gain some help from others when needed :)

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What eigen value for this matix (1 -2) (-2 0)

natali 33 [55]

You find the eigenvalues of a matrix A by following these steps:

Compute the matrix $A' = A-\lambda I$ , where I is the identity matrix (1s on the diagonal, 0s elsewhere)
Compute the determinant of A'
Set the determinant of A' equal to zero and solve for lambda.

So, in this case, we have

$A = \left[\begin{array}{cc}1&-2\\-2&0\end{array}\right] \implies A'=\left[\begin{array}{cc}1&-2\\-2&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right]=\left[\begin{array}{cc}1-\lambda&-2\\-2&-\lambda\end{array}\right]$

The determinant of this matrix is

$\left|\begin{array}{cc}1-\lambda&-2\\-2&-\lambda\end{array}\right| = -\lambda(1-\lambda)-(-2)(-2) = \lambda^2-\lambda-4$

Finally, we have

$\lambda^2-\lambda-4=0 \iff \lambda = \dfrac{1\pm\sqrt{17}}{2}$

So, the two eigenvalues are

$\lambda_1 = \dfrac{1+\sqrt{17}}{2},\quad \lambda_2 = \dfrac{1-\sqrt{17}}{2}$

5 0

3 years ago

Read 2 more answers

A Brooklyn, NY, marketing agency was searching for an account executive. Advertising expenses totaled $13,234 and interviewing e

enot [183]

$13234 + $1328+ $2700 +$7411.55($148231×5%)= $24,673.55

7 0

3 years ago

WHAT IS THE ANSWER TO : 85% IS 20 TO WHAT NUMBER

Ugo [173]

$85\% \ of \ x=20 \\\\ \frac{85}{100}*x=20 \\\\ \frac{17}{20}*x=20 \\\\ \frac{17}{20}=\frac{20}{x} \\\\ x=\frac{20*20}{17} \\\\ \boxed{x=\frac{400}{17}}$