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Determinants

Question
CBSEENMA12034728
Wired Faculty App

Solve system of linear equations,  using matrix method:
5x + 2y = 3
3x + 2y = 5

Solution

The given equations are
5x + 2y = 3
3x + 2y = 5
These equations can be written as
               open square brackets table row 5 cell space space 2 end cell row 3 cell space space 2 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 3 row 5 end table close square brackets
or           AX = B where,
straight A space equals open square brackets table row 5 cell space space 2 end cell row 3 cell space space 2 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 space straight B space equals space open square brackets table row 3 row 5 end table close square brackets 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 5 cell space space space 2 end cell row 3 cell space space space 2 end cell end table close vertical bar space equals space 10 minus 6 space equals space 4 not equal to space 0 space space therefore space space space straight A to the power of negative 1 end exponent space exists. space space space space space space space straight A subscript 11 space equals space 2 comma space space space space straight A subscript 12 space equals space minus 3 comma space space space straight A subscript 21 space equals space minus 2 comma space space space straight A subscript 22 space equals space 5 space therefore space space space adj. space straight A space equals space open square brackets table row cell space space 2 end cell cell space space minus 3 end cell row cell negative 2 end cell cell space space space space 5 end cell end table close square brackets to the power of apostrophe space space equals space open square brackets table row cell space space 2 end cell cell space space space minus 2 end cell row cell negative 3 end cell cell space space space space 5 end cell end table close square brackets 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 fourth open square brackets table row cell space space space 2 end cell cell space space space minus 2 end cell row cell negative 3 end cell cell space space space space 5 end cell end table close square brackets Now space AX space equals space straight B space space rightwards double arrow space space space straight X space equals space straight A to the power of negative 1 end exponent straight B 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 1 fourth open square brackets table row 2 cell space space space minus 2 end cell row cell negative 3 end cell cell space space space space space 5 end cell end table close square brackets space open square brackets table row 3 row 5 end table close square brackets space space space space rightwards double arrow space space open square brackets table row straight x row straight y end table close square brackets space equals space 1 fourth open square brackets table row cell 6 minus 10 end cell row cell negative 9 plus 25 end cell end table close square brackets 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 1 fourth open square brackets table row cell negative 4 end cell row cell space space 16 end cell end table close square brackets space space rightwards double arrow space space 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 negative 1 end cell row cell space space 4 end cell end table close square brackets therefore space space space space space space space straight x space equals space 1 comma space space space space space straight y space equals space 4

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