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Determinants

Question
CBSEENMA12034699
Wired Faculty App

Examine the consistency of the system of equations:
2x – y = 5
x + y = 4

Solution

The given equations are
2x – y = 5
x + y = 4
These equations can be written as
                       open square brackets table row 2 cell space space minus 1 end cell row 1 cell space space space space 1 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 5 row 4 end table close square brackets
or         AX space equals space straight B space where space straight A space equals space open square brackets table row 2 cell space space minus 1 end cell row 1 cell space space space space 1 end cell end table close square brackets comma space 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 space straight B space equals space open square brackets table row 5 row 4 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 space space space space open vertical bar straight A close vertical bar space equals space open vertical bar table row 2 cell space space space minus 1 end cell row 1 cell space space space space space 1 end cell end table close vertical bar space equals space 2 plus 1 space equals space 3 space not equal to space 0
∴   A–1 exists
∴   system of equations has a unique solution, system of equations is consistent.

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