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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?

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


School: Carnegie Mellon University
Department: Engineering
Course: Matrices and Linear Transformations
Professor: Joshua ballew
Term: Spring 2017
Tags: Linear-Algebra
Cost: Free
Name: Matrices and Linear Transformations - 1/18/17
Description: Covers section 1.1 of Lecture on 1/18/17
Uploaded: 01/13/2017
5 Pages 205 Views 7 Unlocks

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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        



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.


Example:         [1]

                [1]  [1]

                [0]     [1]        

Operations of vectors

Case I. Addition of vectors




=        [u1]                [v1]

        | : |                | : |

        [   ]                [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:



        Linear combination of


Proposition I: let c,d


  1. Vector addition is commutative


  1.         [0]


                        |: |


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