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**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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