(3,1), m=2

Sinead Mcgee
2020-10-20
Answered

Write the equation in point-slope form of the line that passes through the given point with the given slope.

(3,1), m=2

(3,1), m=2

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delilnaT

Answered 2020-10-21
Author has **94** answers

y = mx + b

$1=2\times 3+b$

-5 = b

$y=mx+b\ge y=2x-5$

-5 = b

asked 2022-02-23

Here is the example I encountered :

A matrix$M(5\times 5)$ is given and its minimal polynomial is determined to be $(x-2)}^{3$ . So considering the two possible sets of elementary divisors

$\{{(x-2)}^{3},{(x-2)}^{2}\}\text{}\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}\text{}\{{(x-2)}^{3},(x-2),(x-2)\}$

we get two possible Jordan Canonical forms of the matrix , namely$J}_{1$ and $J}_{2$ respectively. So $J}_{1$ has 2 and $J}_{2$ has 3 Jordan Blocks.

Now we are to determine the exact one from these two. From the original matrix M, we determined the Eigen vectors and 2 eigen vectors were linearly independent. So the result is that$J}_{1$ is the one .So, to determine the exact one out of all possibilities , we needed two information -

1) the minimal polynomial ,together with 2) the number of linearly independent eigen vectors.

Now this was a question-answer book so not much theoretical explanations are given . From the given result , I assume the number of linearly independent eigen vectors -which is 2 in this case - decided$J}_{1$ to be the exact one because it has 2 Jordan Blocks. So the equation

"Number of linearly independent eigen vectors=Number of Jordan Blocks"

must be true for this selection to be correct .

Now this equation is not proved in this book or the text book I have read says nothing of this sort

So, that is my question here : How to prove the equation "Number of linearly independent eigen vectors=Number of Jordan Blocks"?

A matrix

we get two possible Jordan Canonical forms of the matrix , namely

Now we are to determine the exact one from these two. From the original matrix M, we determined the Eigen vectors and 2 eigen vectors were linearly independent. So the result is that

1) the minimal polynomial ,together with 2) the number of linearly independent eigen vectors.

Now this was a question-answer book so not much theoretical explanations are given . From the given result , I assume the number of linearly independent eigen vectors -which is 2 in this case - decided

"Number of linearly independent eigen vectors=Number of Jordan Blocks"

must be true for this selection to be correct .

Now this equation is not proved in this book or the text book I have read says nothing of this sort

So, that is my question here : How to prove the equation "Number of linearly independent eigen vectors=Number of Jordan Blocks"?

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A person on an assembly line produces P items per day after t days of training, 400 where $P\left(t\right)=$ How many days of training will it take for a person to $1+23e$ produce 340 items? (Find algebraically.)

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The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y.x,y. or x,y,z.x,y,z. or

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Consider the function $f\left(x\right)=4-5{x}^{2},\text{}\text{}\text{}-3\le x\le 2$ .

The absolute maximum value is$B\otimes$

and this occurs at x=$B\otimes$

The absolute minimum value is$B\otimes$

and this occurs at x=$B\otimes$

The absolute maximum value is

and this occurs at x=

The absolute minimum value is

and this occurs at x=

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For c|| $n\in N\sum _{i=0}^{n}(4i+3)=2{n}^{3}+5n+3$ prove

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