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Determinants

Question
CBSEENMA12034749
Wired Faculty App

Use matrix method to solve the system of equations:
5x - y  = 4
3x + 7y =  10

Solution

The given equations are
5x – y = 4
3x + 7y = 10
These equations can be written as
                       open square brackets table row 5 cell space space space minus 1 end cell row 3 cell space space space space space 7 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 4 row 10 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 5 cell space space space minus 1 end cell row 3 cell space space space space space 7 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 straight B space equals space open square brackets table row 4 row 10 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 5 cell space space minus 1 end cell row 3 cell space space space space space 7 end cell end table close vertical bar space equals space 35 plus 3 space equals space 38 space not equal to 0 therefore space space space 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 space space space space straight A subscript 11 space equals space 7 comma space space space straight A subscript 12 space equals space minus 3 comma space space space space straight A subscript 21 space equals space 1 comma space space space straight A subscript 22 space equals 5 therefore space space space space space space space space space space space space space space adj. space straight A space equals space open square brackets table row 7 cell space space minus 3 end cell row 1 cell space space space space 5 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row 7 cell space space space 1 end cell row cell negative 8 end cell cell space space space space 5 space space 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 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 38 open square brackets table row 7 cell space space space 1 end cell row cell negative 3 end cell cell space space space 5 end cell end table close square brackets Now space space space AX space equals space straight B space space 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 space space space space space space space space space open square brackets table row straight x row straight y end table close square brackets space equals space 1 over 38 open square brackets table row cell space space space 7 end cell cell space space space 1 end cell row cell negative 3 end cell cell space space space 5 end cell end table close square brackets space open square brackets table row 4 row 10 end table close square brackets space space space space space rightwards double arrow space space space space space open square brackets table row straight x row straight y end table close square brackets space equals space 1 over 38 open square brackets table row cell 28 plus 10 end cell row cell negative 12 plus 50 end cell end table close square brackets rightwards double arrow space space space space space space space space space space space space space space space open square brackets table row straight x row straight y end table close square brackets space equals space 1 over 38 open square brackets table row 38 row 38 end table close square brackets space space 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 1 row 1 end table close square brackets therefore space space space space space space space space space space space straight x space equals space 1 comma space space space straight y space equals space 1

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