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3 years ago

Write an equation using the given information. m = -2, b = 4

Mathematics

1 answer:

Oliga [24]3 years ago

5 0

Answer:

y = -2x + 4

Step-by-step explanation:

y = mx +b is slope intercept form so all you have to do is plug in the values. To get y= -2 + 4

Hope that helps and have a great day!

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Sarah exchanged 1,000 US dollars for the Croatian Kuna. The exchange rate was 6.72 Kuna for $1. How many Croatian Kuna did Sarah

AlekseyPX

Answer:

6720 Kuna

Step-by-step explanation:

multiply the rate for one dollar by the amount of money your are converting

6.72 x 1000 = 6720

7 0

3 years ago

(1) (10 points) Find the characteristic polynomial of A (2) (5 points) Find all eigenvalues of A. You are allowed to use your ca

Yuri [45]

Answer:

Step-by-step explanation:

Since this question is lacking the matrix A, we will solve the question with the matrix

$\left[\begin{matrix}4 & -2 \\ 1 & 1 \end{matrix}\right]$

so we can illustrate how to solve the problem step by step.

a) The characteristic polynomial is defined by the equation $det(A-\lambdaI)=0$ where I is the identity matrix of appropiate size and lambda is a variable to be solved. In our case,

$\left|\left[\begin{matrix}4-\lamda & -2 \\ 1 & 1-\lambda \end{matrix}\right]\right|= 0 = (4-\lambda)(1-\lambda)+2 = \lambda^2-5\lambda+4+2 = \lambda^2-5\lambda+6$

So the characteristic polynomial is $\lambda^2-5\lambda+6=0$ .

b) The eigenvalues of the matrix are the roots of the characteristic polynomial. Note that

$\lambda^2-5\lambda+6=(\lambda-3)(\lambda-2) =0$

So $\lambda=3, \lambda=2$

c) To find the bases of each eigenspace, we replace the value of lambda and solve the homogeneus system(equalized to zero) of the resultant matrix. We will illustrate the process with one eigen value and the other one is left as an exercise.

If $\lambda=3$ we get the following matrix

$\left[\begin{matrix}1 & -2 \\ 1 & -2 \end{matrix}\right]$ .

Since both rows are equal, we have the equation

$x-2y=0$ . Thus x=2y. In this case, we get to choose y freely, so let's take y=1. Then x=2. So, the eigenvector that is a base for the eigenspace associated to the eigenvalue 3 is the vector (2,1)

For the case $\lambda=2$ , using the same process, we get the vector (1,1).

d) By definition, to diagonalize a matrix A is to find a diagonal matrix D and a matrix P such that $A=PDP^{-1}$ . We can construct matrix D and P by choosing the eigenvalues as the diagonal of matrix D. So, if we pick the eigen value 3 in the first column of D, we must put the correspondent eigenvector (2,1) in the first column of P. In this case, the matrices that we get are

$P=\left[\begin{matrix}2&1 \\ 1 & 1 \end{matrix}\right], D=\left[\begin{matrix}3&0 \\ 0 & 2 \end{matrix}\right]$

This matrices are not unique, since they depend on the order in which we arrange the eigenvalues in the matrix D. Another pair or matrices that diagonalize A is

$P=\left[\begin{matrix}1&2 \\ 1 & 1 \end{matrix}\right], D=\left[\begin{matrix}2&0 \\ 0 & 3 \end{matrix}\right]$

which is obtained by interchanging the eigenvalues on the diagonal and their respective eigenvectors

4 0

3 years ago

A sports tournament has 6 teams. Each team has the same number of players. There are 60 players total. How many players does eac

Nookie1986 [14]

Answer:

Step-by-step explanation:

because

60:6=10

every team has the same number of players

(it was an easy proble to solve thats why im typing , so i the app can confirm it as an answer)

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5 0

3 years ago

Read 2 more answers

A new car is purchased for $42,000 and over time its value depreciates by one half

MaRussiya [10]

Answer:

t=20

Step-by-step explanation:

delta math blessed.

3 0

3 years ago

50 grams/centimeters= kilograms/meters

Lubov Fominskaja [6]

Answer:

50 grams to kilos is 0.05

50 centimeters to meters is 0.5

4 0

3 years ago