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CMU / Engineering / MAT 241 / What is a directed line segment which corresponds to a displacement?

What is a directed line segment which corresponds to a displacement? Description

Description: Covers section 1.1 of Lecture on 1/18/17
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Lecture 1 Don't forget about the age old question of Describe the 4 branches of chemistry.

Consider the equation Ax=b, in which a,b ∈ R

Case IWe also discuss several other topics like What is the field that looks at interactions among human systems and those found in nature?

When A x x=b/AIf you want to learn more check out What is The Wax argument?

Solution exists is unique

Case II

When A=0, we cant just divide by A

Observe that if b=0 as well, thenWe also discuss several other topics like log3 1 81

(0)x=0, so x can be every real value

Existence of solutions but there is no uniquenessIf you want to learn more check out What is the global definition of accounting?

Case III

When A=0 and b0, thenIf you want to learn more check out What is a spyware?

(0)x=b, so therefore we have no solution to the problem

To generalize the version of Ax=B, we are instead of going to look for real number take x to be a real value vector.

Intuition: vectors in

Here we have . they name the same displacement and are equal

Denote vectors using lower case letter with either “hook” or boldface.

Since we can identify a vector with a point in the plane (a,b) by starting the vector of the origin, if with (a,b) then

[a]

[b]

Generalization - vectors in IRN

RN =         {[a1]                                }

{[a2]L a;        }

{[:  ]                                }

{[an]                                }

When are two vectors equal to each other?

Def: let

We say if and only if

Each i=1,2..n.

Note:

Example:         [1]

[1]  [1]

[0]     [1]

Operations of vectors

Let

Example

=        [u1]                [v1]

| : |                | : |

[   ]                [vn]

[u1+v1]

|   :    |

|   :    |

[un+vn]

Case II scalar multiplication

Let         [u1 ]

| :  |        = IRn

[un ]

Let c

Scalar multiplication

[cu1 ]

| :    |

[cun ]

For c > 1, then…

For c(0,1) then…

For c < 0, then…

Cut points in the opposite direction of , factor still applied

Subtraction of vectors

Linear combination:

Let

Let

Linear combination of

Proposition I: let c,d

Then

()

1.         [0]

|0|

|: |

[0]

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