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Agata [3.3K]
3 years ago
8

Find all of the eigenvalues λ of the matrix A. (Hint: Use the method of Example 4.5 of finding the solutions to the equation 0 =

det(A − λI). Enter your answers as a comma-separated list.) A = 3 5 8 0
Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
8 0

Answer:

\lambda=8,\ \lambda=-5

Step-by-step explanation:

<u>Eigenvalues of a Matrix</u>

Given a matrix A, the eigenvalues of A, called \lambda are scalars who comply with the relation:

det(A-\lambda I)=0

Where I is the identity matrix

I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]

The matrix is given as

A=\left[\begin{array}{cc}3&5\\8&0\end{array}\right]

Set up the equation to solve

det\left(\left[\begin{array}{cc}3&5\\8&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda \end{array}\right]\right)=0

Expanding the determinant

det\left(\left[\begin{array}{cc}3-\lambda&5\\8&-\lambda\end{array}\right]\right)=0

(3-\lambda)(-\lambda)-40=0

Operating Rearranging

\lambda^2-3\lambda-40=0

Factoring

(\lambda-8)(\lambda+5)=0

Solving, we have the eigenvalues

\boxed{\lambda=8,\ \lambda=-5}

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Which inequality matches the given situation if w represents weight in pounds:Baby tigers can be no larger than 4 pounds.
ozzi

Given:

w be the weight in pounds of a baby tigers.

To find:

The inequality if baby tigers can be no larger than 4 pounds.

Solution:

Baby tigers can be no larger than 4 pounds. It mean weight of baby tigers cannot be greater than 4. In other words, the weight of the baby tigers must be less than or equal to 4.

Let w represents weight in pounds and the weight of the baby tigers must be less than or equal to 4. So,

w\leq 4

Therefore, the required inequality is w\leq 4.

4 0
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The initial deposit into an account?
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Answer:

B

Step-by-step explanation:

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8 0
3 years ago
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svlad2 [7]

Answer: Solve for m m by simplifying both sides of the equation, then isolating the variable. m=15

Step-by-step explanation: Reducing to lowest terms On both sides

8 0
3 years ago
Can someone answer fast.plsss
Anika [276]

Answer:

a

Step-by-step explanation:

sec (thita) = squrt (5)

squaring on both sides:

sec^2 (thita) = 5 - equation 1

1 + tan^2 (thita) = 5

tan^2 (thita) = 4

tan (thita) = 2.

= tan (thita) - squrt(5)sin(thita)

= 2 - squrt(5) x 2/ squrt(5)

= 0

from eqn - 1

sec(thita) = squrt(5)

cos(thita) = 1/ squrt(5)

sin(thita) = squrt ( 1- 1/(squrt (5))^2)

sin(thita) = 2/ squrt(5) .

4 0
3 years ago
I will give brainelest but i need help on the graph
const2013 [10]

Answer:

1)   (6,2) (9,2) (3,8) (3,5)

2)   (2,-5) (5,-5) (-1,-11) (-1,-8)

Step-by-step explanation:

For the first question, your reflecting over the x-axis into quadrant I, so you just need to make all the coordinates positive.  The numbers stay the same - you just get rid of the negative signs.  (6,2) (9,2) (3,8) (3,5)

For the second problem, you subtract 4 from the x-value, and 3 from the y-value.

(6,-2) becomes (2,-5)

(9,-2) becomes (5,-5)

(3,-8) becomes (-1,-11)

(3,-5)  becomes (-1,-8)

3 0
3 years ago
Read 2 more answers
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