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astra-53 [7]
2 years ago
15

Can anybody help me with these three problems thank you

Mathematics
1 answer:
Amiraneli [1.4K]2 years ago
8 0

Answer:

1) 1/7

2) 1/3

3) 1/4

Step-by-step explanation:

1) Since there are 7 days in a week it can be expressed as the fraction 1/7

2) Since there are 3 feet in a yard it can be expressed as the fraction 1/3

3) Since there are 4 quarts in a gallon it can be expressed as the fraction 1/4

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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 =
Svetradugi [14.3K]

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}

8 0
3 years ago
Factor the expression completely I’ve the complex numbers X^4+10x^2+25
Elza [17]

We have

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so that with a = x² and b = 5, we have

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Next, we have

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so that with a = x and b = √5 i,

x² + 5 = x² - (-5) = (x - √5 i) (x + √5 i)

So, the complete factorization over the complexes is

(x - √5 i)² (x + √5 i)²

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