Express 0.000023 in standard form . *

Could someone help with this and provide the working out too

GalinKa [24]

$-3$

4 0

2 years ago

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What is the volume of metal in the pipe? Use 3.14 for a and

aleksandr82 [10.1K]

I need another number for this problem to answer

4 0

3 years ago

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(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

Need help with this ASAP ILL LOVE U FOREVER

Paha777 [63]

Answer:its easy it the first one you had posted

Step-by-step explanation:

7 0

3 years ago

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Been trying at this can't please help lol

xz_007 [3.2K]

To add or sum this arrary, beg ∈ {array} {r} 37 \202\ + 160/ ∈ end {array} gives <u>A) 399</u>.

<h3>What is an array?</h3>

An array is a data structure made up of some elements.

The sum of all elements in an array is found by adding up the elements in the array.

<h3>Data and Calculations:</h3>

Elements of the array = 37, 202, and 160

The sum of the array, 37 + 202 + 160 = 399

Thus, to add or sum this arrary, beg ∈ {array} {r} 37 \202\ + 160/ ∈ end {array} gives <u>A) 399</u>.

Learn more about arrays at brainly.com/question/23698059

#SPJ1

<h3>Question:</h3>

Add beg ∈ {array} {r} 37 \202\ + 160/ ∈ end {array}

<h3>Answer Options:</h3>

A) 399

B) 389

C) 400

D) 409

4 0

1 year ago

Express 0.000023 in standard form . *​

Express 0.000023 in standard form . *