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Lecture

MAT223H1 Lecture Notes - Main Diagonal, Mexican Peso, Algebraic Structure

Department
Mathematics
Course Code
MAT223H1
Professor
all

This preview shows page 1. to view the full 4 pages of the document. MAT 223
Definition
A linear system with m equations and n variables is the following set:
a1x1 + a2x2 + ... + anxn = b1
m a1x1 + a2x2 + ... + anxn = b2
...
a1x1 + a2x2 + ... + anxn = bm
A solution is a vector (t1,t2,...,tn) є Rn that satisfies all the equations.
If the set of solutions is S = Ø then we say that the system is inconsistent.
Note that the above system can be represented as follows:
a11 a12 ... a1n | b1
a21 a22 ... a2n | b2
...
am1 am2 ... amn | bm
Definition
Two systems of linear equations are said to be equivalent if and only if they have
the same set of solutions.
Matrix Main diagonal of c is (1 8 4)
C = 1 0 6 C є M3x3
7 8 3 C is a square Matrix order 3
9 6 4
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