18.06.02: Vectors
Lecturer: Barwick
Wednesday 05 February 2016
18.06.02: Vectors
Lines vs. vectors
A vector is a list of real numbers
1
= ( 2 ) .
We draw this vector as an arrow pointing from the point (0, 0, , 0) to the
point (1 , 2 , , ):
. (0, 0, , 0)

18.06.08: Inverting
matrices
Lecturer: Barwick
Monday 22 February 2016
18.06.08: Inverting matrices
Suppose
11 12
22
= ( 21
1 2
1
2
)
an (square!) matrix. We contemplate via the map R
R .
18.06.08: Inverting matrices
Recall that is defined by the

18.06.04: Matrices
Lecturer: Barwick
Wednesday 10 February 2016
18.06.04: Matrices
Figure 1: What are the angles between my bonds?
You were saying?
18.06.04: Matrices
Exam 1 is a week from today
It should be pretty simple.
I will cover the course materi

18.06.03: Length and angle
Lecturer: Barwick
Monday 08 February 2016
18.06.03: Length and angle
1
The length of a vector = ( 2 ) R is defined using the good old law
of Pythagoras:
12 + 22 + + 2 .
Geometrically, it works exactly as we expect its the lengt

18.06.05: Systems of linear
equations as matrices
Lecturer: Barwick
Friday 12 February 2016
18.06.05: Systems of linear equations as matrices
Suppose
11 12
22
= ( 21
1 2
1
2
)
an matrix, and
1
( 2 ) R
a vector.
18.06.05: Systems of linear equatio

18.06.10: Spaces of vectors
Lecturer: Barwick
Friday 26 February 2016
18.06.10: Spaces of vectors
Another day, another system of linear equations.
0 = 12 + 11 17;
0 = 2 + 9;
0 = 3 + 4 + 5.
Solve it!
18.06.10: Spaces of vectors
The rows are not linearly in