MIT - Massachusetts Institute of Technology

# Lec 1 | MIT 18.06 Linear Algebra, Spring 2005

Lecture 1: The Geometry of Linear Equations.
View the complete course at: http://ocw.mit.edu/18-06S05

More courses at http://ocw.mit.edu

• i'm from india and i have learned this in high school.﻿

• This is crazy, the link below has the syllabus, readings from the book, which he wrote.
In addition all the readings from said book, exams including the final, with…..drum roll please.. the solutions.
This is just First Class.﻿

• Thank you for making this class available. This professor is awesome.﻿

• Bless you MIT. Over here in Georgia (country not a state of US) our lectors don't really explain it all that well and there is basically no literature to read upon subjects. you guys are godsend.﻿

• The only thing I don't understand from this video is just how the x coefficients of A can be represented as a vector with x AND y components . . . it almost seems as if you magically get y components from x components that are seemingly unrelated . . .﻿

• The emphasis on "Column picture" expressed as a linear combination is a valuable insight.﻿

• 这是我最喜欢的线性代数的公开课，学的很轻松！﻿

• Prof.Strang is amazing, competent teacher who deserves the title of professor.﻿

• I wonder if these math people at MIT can work out how long it will take to pay off their student loans﻿

• muito bom! mas gostaria de saber pra que serve isso tudo!﻿

• Proof 2x-y=0 -x+2y=3
2x=y
-x + 2y =3
-x + 2(2x) = 3
-x + 4x = 3
3x = 3
x = 1
2x=y x=1 2(1)=y y=2

Proof 2x-y=0 -x+2y-z=-1 -3y+4z=4
y=2x
-x + 2(2x) -z = -1
-x + 4x -z = -1
3x -z = -1
-z = -1-3x
z = 1+3x

-3y + 4z = 4
-3(2x) + 4 (1+3x) = 4
-6x + 4 + 12x = 4
6x = 4 – 4 = 0
x = 0
2x=y x=0 2(0)=y y=0
2x-y=0 2(0)-0=0

z = 1+3x = 1+3(0) = 1+0 = 1

-x + 2y = -1
-0 + 2(0) -z = -1
-z = -1
z=1

-3y+4z=4 y=0 It will be -3(0) + 4z = 4
z = 1

So x=y=0 z=1﻿

• If you want to get an intuition for matrices and what they represent, what inverses, determinants and eigenvectors/eigenvalues really reflect, watch this absolutely brilliant video series by 3Blue1Brown:

(15 videos of ~10min average length)

You will see through the number jungle and understand what is going on underneath. It will be clear WHY e.g. there are no inverses for matrices where the determinant is zero. You'll see that it couldn't be any other way.

3Blue1Brown barely ever touches the nitty gritty. You'd need to (re)watch this MIT course to know how to juggle the numbers around, but you'd have a much better appreciation for what you are doing to those matrices.

I honestly can't recommend it enough!﻿

• Greetings professor and congratulations for this excellent course i wish i could have seen this videos before i started my algebra lineal course you are great keep spreading the knowledge!﻿

• I wonder from where around the world students watch those videos
I'm from the MUAS (Munich, Germany) and our linear Algebra courses are based on Strangs book and basically the same as those video lectures, tho I prefer them since he is better at explaining something without being boring﻿

• Amazing way of explaining it﻿

• This is the single best source of linear algebra knowledge on the planet, this set of videos. And it's completely free.﻿

• I found " Column picture " may be the shortcut to find the values of X,Y faster what you say !!!﻿

• thanks a lot professor you are writing for us to see while another teachers writing for their selves by writing a little writing that students can't see.﻿

• Awesome lecture, can't be any better!
Thanks MIT OpenCourseWare.﻿

• The subtitle is not match the voice of the teacher.
The subtitle is more faster. One sentence is disappear, then the teacher start to say that sentence.
Could you adjust the schedule of the subtitle for this video ? thanks﻿

• Linear Algebra rules!
Until you discover that most real-world systems are non-linear.﻿