How to perform elementary operations on matrices ?

Asked by jyotigupta171 | 9th Jun, 2015, 07:20: PM

Expert Answer:

Find space the space inverse space of space straight A equals open square brackets table row 1 3 3 row 1 4 3 row 1 3 4 end table close square brackets  In space order space to space use space elementary space row space operations comma space write space straight A equals IA  open square brackets table row 1 3 3 row 1 4 3 row 1 3 4 end table close square brackets equals open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets straight A rightwards double arrow open square brackets table row 1 3 3 row 0 1 0 row 0 0 1 end table close square brackets equals open square brackets table row 1 0 0 row cell negative 1 end cell 1 0 row cell negative 1 end cell 0 1 end table close square brackets straight A space space open square brackets Applying space straight R subscript 2 left right arrow straight R subscript 2 minus straight R subscript 1 comma space straight R subscript 3 left right arrow straight R subscript 3 minus straight R subscript 1 close square brackets rightwards double arrow open square brackets table row 1 0 3 row 0 1 0 row 0 0 1 end table close square brackets equals open square brackets table row 4 cell negative 3 end cell 0 row cell negative 1 end cell 1 0 row cell negative 1 end cell 0 1 end table close square brackets straight A open square brackets Applying space straight R subscript 1 left right arrow straight R subscript 1 minus 3 straight R subscript 2 close square brackets rightwards double arrow open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets equals open square brackets table row 7 cell negative 3 end cell cell negative 3 end cell row cell negative 1 end cell 1 0 row cell negative 1 end cell 0 1 end table close square brackets straight A open square brackets Applying space straight R subscript 1 left right arrow straight R subscript 1 minus 3 straight R subscript 3 close square brackets therefore straight A to the power of negative 1 end exponent equals open square brackets table row 7 cell negative 3 end cell cell negative 3 end cell row cell negative 1 end cell 1 0 row cell negative 1 end cell 0 1 end table close square brackets

Answered by Prasenjit Paul | 10th Jun, 2015, 09:11: AM

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