Math Assignment Help With System Of Linear Equation
3.7.3 System of linear equation:
22.214.171.124 Linear equation in matrix notation: take the following system of linear equation;
a21x+a22x+....+a2nxn = b2
........ .... .... ... ... ... ....
... ... ... ... .... .... .... ....
an1x+an2x+....+annxn = bn
The above system can also be written in the form;
AX = B
It can be rearranged as;
Let X = X1 and X = X2 be two solutions of AX = B
AX1 = B and AX2 = B
AX1 = AX2
Since A being invertible, by cancellation law, we have;
X1 = X2
Hence the given system of equation has unique solution.
Criterion for a given system of equation to have unique solution:
i) If |A| ≠ 0, then the system is consistent and has a unique solution and is given by
X = A-1B
- ii) If |A| = 0 and (adjA) B ≠ 0, then the system is inconsistent.
- iii) If |A| = 0 and (adjA) B = 0 then the system is consistent and has infinitely many solution.
Example: Using matrix method, solve the system of linear equation;
5x + 3y + 2 = 0
2x + 3y + 3= 0
Solution: the given set equations are
5x + 7y + 2 = 0
2x + 3y + 3= 0
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