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Determinants

Question
CBSEENMA12034697
Wired Faculty App

Examine the consistency of the system of equations:
x + 2y = 2
2x + 3y = 3 

Solution

The given equations are
x + 2y = 2    
2x + 3y = 3
These equations can be written as
            open square brackets table row 1 cell space space space 2 end cell row 2 cell space space space 3 end cell end table close square brackets space open square brackets table row straight x row straight y end table close square brackets space equals space open square brackets table row 2 row 3 end table close square brackets
 or space AX space equals space straight B space where space straight A space equals space open square brackets table row 1 cell space space 2 end cell row 2 cell space space 3 end cell end table close square brackets comma space space straight X space equals space open square brackets table row straight x row straight y end table close square brackets comma space space straight B space equals space open square brackets table row 2 row 3 end table close square brackets space space space space space space space space space space space space space space space space space space space space open vertical bar straight A close vertical bar space equals space open vertical bar table row 1 cell space space space 2 end cell row 2 cell space space space 3 end cell end table close vertical bar space equals space 3 minus 4 space equals space minus 1 space not equal to space 0 space
∴   A–1 exists
∴ system of equations has a unique solution
∴  system of equations is consistent.

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