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Determinants

Question
CBSEENMA12034722
Wired Faculty App

Solve system of linear equations,  using matrix method:
2x - y = -2
3x + 4y = 3

Solution

The given equations are
2x – y = –2
3x + 4y = 3
These equations can be written as
                  open square brackets table row 2 cell space space space minus 1 end cell row 3 cell space space space space space 4 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 cell negative 2 end cell row cell space space 3 space end cell end table close square brackets
or          AX = B where straight A space equals space open square brackets table row 2 cell space space minus 1 end cell row 3 cell space space space space 4 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 space space straight B space equals space open square brackets table row cell negative 2 end cell row cell space space 3 end cell end table close square brackets
   open vertical bar straight A close vertical bar space equals space open vertical bar table row 2 cell space space minus 1 end cell row 3 cell space space space space 4 end cell end table close vertical bar space equals space 8 plus 3 space equals space 11 space not equal to space 0 therefore space space space space space straight A to the power of negative 1 end exponent space exists. space space space space space space space space straight A subscript 11 space equals space 4 comma space space space space space straight A subscript 12 space equals space minus 3 comma space space space straight A subscript 21 space equals space 1 comma space space straight A subscript 21 space equals space 2 space space space space space space space space adj. space straight A space equals space open square brackets table row 4 cell space space minus 3 end cell row 1 cell space space space space 4 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row cell space 4 end cell cell space space space 1 end cell row cell negative 3 end cell cell space space space 2 end cell end table close square brackets space space space space space space space space straight A to the power of negative 1 end exponent space equals space fraction numerator adj. space straight A over denominator open vertical bar straight A close vertical bar end fraction space equals space 1 over 11 open square brackets table row 4 cell space space space space 1 end cell row cell negative 3 end cell cell space space space 2 end cell end table close square brackets Now comma space space space AX space equals space straight B space space space rightwards double arrow space space space space straight X space equals space straight A to the power of negative 1 end exponent straight B
rightwards double arrow space space space open square brackets table row straight x row straight y end table close square brackets space equals space 1 over 11 open square brackets table row 4 cell space space space 1 end cell row cell negative 3 end cell cell space space space 2 end cell end table close square brackets space open square brackets table row cell negative 2 end cell row cell space 3 end cell end table close square brackets space space rightwards double arrow space space space space open square brackets table row straight x row straight y end table close square brackets space equals space 1 over 11 open square brackets table row cell negative 8 plus 3 end cell row cell space 6 plus 6 end cell end table close square brackets rightwards double arrow space space space open square brackets table row straight x row straight y end table close square brackets space equals 1 over 11 open square brackets table row cell negative 5 end cell row cell space 12 end cell 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 rightwards double arrow space space space space open square brackets table row straight x row straight y end table close square brackets space equals space open square brackets table row cell fraction numerator negative 5 over denominator 11 end fraction end cell row cell 12 over 11 end cell end table close square brackets therefore space space space space straight x space equals space minus 5 over 11 comma space space space straight y space equals space 12 over 11

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