Solve by matrix method: 2x+y+2z=5, x-y-z=0, x+2y+3z=5.

Asked by ppgm11patil | 29th Oct, 2018, 02:21: PM

Expert Answer:

2 x plus y plus 2 z equals 5
x minus y minus z equals 0
x plus 2 y plus 3 z equals 5

m a t r i x space w i l l space b e
left square bracket table row 2 1 2 row 1 cell negative 1 end cell cell negative 1 end cell row 1 2 3 end table right square bracket left square bracket table row x row y row z end table space right square bracket equals left square bracket table row 5 row 0 row 5 end table right square bracket

R subscript 2 equals 2 R subscript 2 minus R subscript 1 space end subscript comma space R subscript 3 equals 2 R subscript 3 minus R subscript 1
left square bracket table row 2 1 2 row 0 cell negative 3 end cell cell negative 4 end cell row 0 3 4 end table right square bracket left square bracket table row x row y row z end table right square bracket equals left square bracket table row 5 row cell negative 5 end cell row 5 end table right square bracket

n o w space R subscript 3 equals R subscript 3 plus R subscript 2
left square bracket table row 2 1 2 row 0 cell negative 3 end cell cell negative 4 end cell row 0 0 0 end table right square bracket left square bracket table row x row y row z end table right square bracket equals left square bracket table row 5 row cell negative 5 end cell row 0 end table right square bracket

h e n c e space w e space g e t space space 2 x plus y plus 2 z equals 5
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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 space space 0 equals 0
h e n c e space t h e r e space a r e space i f n i t e l y space m a n y space s o l u t i o n space t a k e space z equals 2 space t h e n space y equals negative 1 space a n d space space t h e n space x equals 1
i f space w e space c h a n g e space t h e space v a l u e space o f space z space w e space g e t space i n f i n e t e l y space m a n y space s o l u t i o n.

Answered by Ram Singh | 29th Oct, 2018, 05:03: PM