linear algebra week3 matrices

Matrices, vectors, and solving simultaneous equation problems

matrices(6 + 9 matrix) = 15
1.rotate and stretch vectors.
2.help solve simultaneous equations.

manipulating(2) = 2
simultaneous(5) = 5

transform(6) = 6 how vectors are transformed by matrices
matrix * vector = vector

matrix * unit basis vector =

Types of matrix transformation

matrix(14) = 14
different kinds of matrices
1. Identity Matrix(does nothing and leaves everything preserved)
basic vectors of the space (1 0)
(0 1)
2. Diagonal Matrix
3. Inversion Matrix

fraction(2) = 2
invert(2 + 3 inversion) = 5

mirror(8) = 8
shear(8) = 9
rotation(11) = 11

Solving the apples and bananas problem: Gaussian elimination

inverse(12) = 12
identity(6) = 6
carrot(6) = 6

elimination(2) = 2
substitution(3) = 3
Echelon form(1) = 1

Going from Gaussian elimination to finding the inverse matrix

inverse(14) = 14
general(5) = 5
identity(13) = 13

AB=I,B is the inverse matrix of A
computationally(2) = 2

Determinants and inverses

determinant(20) = 20
scale(1) = 1

inverse(5) = 5
And by dividing by the determinant, we're normalizing the space back to its original size.

collapse(7) = 7

Another way of looking at this is the inverse matrix let's me undo my transformation.
It lets me get from the new vectors back to the original vectors.But if I have dumped the dimension, if I have scrapped dimension by turning 2D space into a line, or a 3D space into a plane or a line, I can't undo that anymore.