Equality of Vectors:
Definition 1:
Vectors V=(a,b,c,...,z) and W=(1,2,3,4,5,...,n) are said to be equivalent if a=1 ; b=2 ; c=3 ; ...
We indicate the equality by writing V=W
Definition 2:
V+W= (a+1, b+2, ...,Z+n)
KV= (Ka, Kb, Kc, ..., Kn)
-V=(-a,-b,-c,...,-z)
Notification:
As far as we know there are two notations for vectors:
The comme delimited form: V=(a,b,c,...,z) also called the row vector form
The column vector form
Will start this cours by an Introduction to matrices:
Elementary row operations:
Echelon Forms:
Before getting started with Jordan and Gaussian you have first to learn some properties about echelon forms:
A matrix is in Row Echelon Form if:
A matrix is in Reduced Row Echelon Form if:
Augmented Matrices and Jordan-Gausse and Gaussian elimination:
Solving Linear Systems by Row Reduction:
Matrix Operations:
The Trace:
If A is a square matrix, then the trace of A, denoted by tr(A), is defined to be the sum of the entries on the main diagonal of A.
Zero matrix VS Identity matrix
Inverse of Matrix: Theory
Inverse of a 2 by 2 Matrix:
The inverse of a matrix using row operations.
here it's a 3 by 3 but it workes for all the sizes
Properties of Diagonal Matrix and Transpose:
Elementary matrices; A method for finding the inverse of the matrix A
Solving Linear Systems by matrix inversion:
Subspace
Spaning and Basis
Some practice:
This is it.The End
This is almost all about Mat 120, we hope that you enjoyed our company and that you took full advantage of what we presented to you.
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