using matrices solve :
 
                                2x + 3y + 32 = 5
                                x - 2y + 2 = -4
                                3x - y - 22 = 3

Asked by Lochana Jayachandran | 5th Oct, 2014, 07:15: PM

Expert Answer:

begin mathsize 12px style open square brackets table row 2 3 3 row 1 cell minus 2 end cell 1 row 3 cell minus 1 end cell cell minus 2 end cell end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row 5 row cell minus 4 end cell row 3 end table close square brackets A p p l y i n g space R subscript 1 space left right arrow space R subscript 2 open square brackets table row 1 cell minus 2 end cell 1 row 2 3 3 row 3 cell minus 1 end cell cell minus 2 end cell end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row cell minus 4 end cell row 5 row 3 end table close square brackets  A p p l y i n g space R subscript 2 space rightwards arrow R subscript 2 space minus space 2 left parenthesis R subscript 1 right parenthesis comma space space R subscript 3 space rightwards arrow R subscript 3 space minus space 3 left parenthesis R subscript 1 right parenthesis  open square brackets table row 1 cell minus 2 end cell 1 row 0 7 1 row 0 5 cell minus 5 end cell end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row cell minus 4 end cell row 13 row 15 end table close square brackets  A p p l y i n g space R subscript 2 space rightwards arrow space 1 over 7 left parenthesis R subscript 2 right parenthesis open square brackets table row 1 cell minus 2 end cell 1 row 0 1 cell 1 over 7 end cell row 0 5 cell minus 5 end cell end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row cell minus 4 end cell row cell 13 over 7 end cell row 15 end table close square brackets  A p p l y i n g space R subscript 1 rightwards arrow space R subscript 1 space plus space 2 left parenthesis R subscript 2 right parenthesis comma space R subscript 3 space rightwards arrow space R subscript 3 space minus space 5 left parenthesis R subscript 2 right parenthesis open square brackets table row 1 0 cell 9 over 7 end cell row 0 1 cell 1 over 7 end cell row 0 0 cell fraction numerator minus 40 over denominator 7 end fraction end cell end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row cell minus 2 over 7 end cell row cell 13 over 7 end cell row cell 40 over 7 end cell end table close square brackets  A p p l y i n g space R subscript 3 space rightwards arrow space fraction numerator minus 7 over denominator 40 end fraction cross times R subscript 3 open square brackets table row 1 0 cell 9 over 7 end cell row 0 1 cell 1 over 7 end cell row 0 0 1 end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row cell minus 2 over 7 end cell row cell 13 over 7 end cell row cell minus 1 end cell end table close square brackets  A p p l y i n g space R subscript 2 rightwards arrow space R subscript 2 space minus space 1 over 7 left parenthesis R subscript 3 right parenthesis comma space R subscript 1 space rightwards arrow space R subscript 1 space minus space 9 over 7 left parenthesis R subscript 3 right parenthesis open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row 1 row 2 row cell minus 1 end cell end table close square brackets  therefore x space equals space 1 comma space y space equals space 2 space a n d space z space equals space minus 1 end style

Answered by Mili Hariyani | 6th Oct, 2014, 12:30: PM

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