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using the elementry tranformations,find the inverse of the matrix  open square brackets table row 1 3 cell negative 2 end cell row cell negative 3 end cell 0 cell negative 5 end cell row 2 5 0 end table close square brackets

Asked by Manisha Marwaha 13th March 2015, 6:29 PM
Answered by Expert
Answer:

HiA equals space open square brackets table row 1 3 cell negative 2 end cell row cell negative 3 end cell 0 cell negative 5 end cell row 2 5 0 end table close square brackets A A to the power of negative 1 end exponent equals space I space open square brackets table row 1 3 cell negative 2 end cell row cell negative 3 end cell 0 cell negative 5 end cell row 2 5 0 end table close square brackets A to the power of negative 1 end exponent equals space open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets  R subscript 2 plus 3 R subscript 1 comma space space space R subscript 3 minus 2 R subscript 1 open square brackets table row 1 3 cell negative 2 end cell row 0 9 cell negative 11 end cell row 0 cell negative 1 end cell 4 end table close square brackets A to the power of negative 1 end exponent space equals space open square brackets table row 1 0 0 row 3 18 cell negative 17 end cell row cell negative 2 end cell cell negative 7 end cell 8 end table close square brackets R subscript 2 over 9 open square brackets table row 1 3 cell negative 2 end cell row 0 1 cell fraction numerator negative 11 over denominator 9 end fraction end cell row 0 cell negative 1 end cell 2 end table close square brackets A to the power of negative 1 end exponent space space equals space open square brackets table row 1 0 0 row cell 1 third end cell 2 cell fraction numerator negative 17 over denominator 9 end fraction end cell row 0 cell negative 1 end cell 2 end table close square brackets R subscript 1 plus 3 R subscript 3 comma space space space end subscript R subscript 3 plus R subscript 2 open square brackets table row 1 0 10 row 0 1 cell fraction numerator negative 11 over denominator 9 end fraction end cell row 0 0 2 end table close square brackets A to the power of negative 1 end exponent equals space space open square brackets table row 1 cell negative 3 end cell 6 row cell 1 third end cell 2 cell fraction numerator negative 17 over denominator 9 end fraction end cell row cell 1 third end cell 1 cell 1 over 9 end cell end table close square brackets R subscript 3 over 2 open square brackets table row 1 0 10 row 0 1 cell fraction numerator negative 11 over denominator 9 end fraction end cell row 0 0 1 end table close square brackets A to the power of negative 1 end exponent space equals space space open square brackets table row 1 cell negative 3 end cell 6 row cell 1 third end cell 2 cell fraction numerator negative 17 over denominator 9 end fraction end cell row cell 1 over 6 end cell cell 1 half end cell cell 1 over 18 end cell end table close square brackets R subscript 1 minus 10 R subscript 3 comma space space space R subscript 2 plus 11 over 9 R subscript 3 S O L V I N G space F U R T H E R space Y O U space W I L L space G E T space T H E space A N S

Answered by Expert 13th March 2015, 6:51 PM
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