Solve by matrix.
2/x + 3/y + 10/z = 4
4/x -  6/y + 5/z  = 1  

Asked by Ayush Jaiswal | 11th Sep, 2016, 09:06: AM

Expert Answer:

One of the equations is missing. Im guessing that you have not typed the third equation otherwise it is not possible to solve.
begin mathsize 16px style Equations space 2 over straight x plus 3 over straight y plus 10 over straight z equals 4 comma space 4 over straight x minus 6 over straight y plus 5 over straight z equals 1 space and space 6 over straight x plus 9 over straight y minus 20 over straight z equals 2 space can space be space written space as space follows.
open square brackets table row 2 3 10 row 4 cell negative 6 end cell 5 row 6 9 cell negative 20 end cell end table close square brackets open square brackets table row cell 1 over straight x end cell row cell 1 over straight y end cell row cell 1 over straight z end cell end table close square brackets equals open square brackets table row 4 row 1 row 2 end table close square brackets space that space is space of space the space form space AX space equals space straight B space where space straight A space equals open square brackets table row 2 3 10 row 4 cell negative 6 end cell 5 row 6 9 cell negative 20 end cell end table close square brackets comma space straight X equals open square brackets table row cell 1 over straight x end cell row cell 1 over straight y end cell row cell 1 over straight z end cell end table close square brackets space and space straight B equals open square brackets table row 4 row 1 row 2 end table close square brackets space
straight X equals fraction numerator adjA over denominator open vertical bar straight A close vertical bar end fraction straight B
straight a subscript 11 equals left parenthesis negative 1 right parenthesis to the power of 1 plus 1 end exponent open vertical bar table row cell negative 6 end cell 5 row 9 cell negative 20 end cell end table close vertical bar equals 120 minus 45 equals 75 comma space space space straight a subscript 12 equals left parenthesis negative 1 right parenthesis to the power of 1 plus 2 end exponent open vertical bar table row 4 5 row 6 cell negative 20 end cell end table close vertical bar equals minus left square bracket negative 80 minus 30 right square bracket equals 110 comma space space space space straight a subscript 13 equals left parenthesis negative 1 right parenthesis to the power of 1 plus 3 end exponent open vertical bar table row 4 cell negative 6 end cell row 6 9 end table close vertical bar equals 36 plus 36 equals 72
straight a subscript 21 equals left parenthesis negative 1 right parenthesis to the power of 2 plus 1 end exponent open vertical bar table row 3 10 row 9 cell negative 20 end cell end table close vertical bar equals minus left square bracket negative 60 minus 90 right square bracket equals 150 comma space space space straight a subscript 22 equals left parenthesis negative 1 right parenthesis to the power of 2 plus 2 end exponent open vertical bar table row 2 10 row 6 cell negative 20 end cell end table close vertical bar equals minus 40 minus 60 equals negative 100 comma space space straight a subscript 23 equals left parenthesis negative 1 right parenthesis to the power of 2 plus 3 end exponent open vertical bar table row 2 3 row 6 9 end table close vertical bar equals minus left square bracket 18 minus 18 right square bracket equals 0
straight a subscript 31 equals left parenthesis negative 1 right parenthesis to the power of 3 plus 1 end exponent open vertical bar table row 3 10 row cell negative 6 end cell 5 end table close vertical bar equals 15 plus 60 equals 75 comma space space straight a subscript 32 equals left parenthesis negative 1 right parenthesis to the power of 3 plus 2 end exponent open vertical bar table row 2 10 row 4 5 end table close vertical bar equals minus left square bracket 10 minus 40 right square bracket equals 30 comma space space space straight a subscript 33 equals left parenthesis negative 1 right parenthesis to the power of 3 plus 3 end exponent open vertical bar table row 2 3 row 4 cell negative 6 end cell end table close vertical bar equals minus 12 minus 12 equals negative 24
So comma space cofactor space matrix space of space straight A equals open square brackets table row 75 110 72 row 150 cell negative 100 end cell 0 row 75 30 cell negative 24 end cell end table close square brackets rightwards double arrow adjA equals open square brackets table row 75 150 75 row 110 cell negative 100 end cell 30 row 72 0 cell negative 24 end cell end table close square brackets space
and space open vertical bar table row 75 150 75 row 110 cell negative 100 end cell 30 row 72 0 cell negative 24 end cell end table close vertical bar equals 75 left parenthesis 2400 minus 0 right parenthesis minus 150 left parenthesis negative 2640 minus 2160 right parenthesis plus 75 left parenthesis 0 plus 7200 right parenthesis equals 180000 plus 720000 plus 540000 equals 1440000
So comma space straight X equals 1 over 1440000 open square brackets table row 75 150 75 row 110 cell negative 100 end cell 30 row 72 0 cell negative 24 end cell end table close square brackets open square brackets table row 4 row 1 row 2 end table close square brackets equals 1 over 1440000 open square brackets table row 600 row 400 row 240 end table close square brackets equals open square brackets table row cell 1 over 2400 end cell row cell 1 over 3600 end cell row cell 1 over 6000 end cell end table close square brackets
rightwards double arrow open square brackets table row cell 1 over straight x end cell row cell 1 over straight y end cell row cell 1 over straight z end cell end table close square brackets equals open square brackets table row cell 1 over 2400 end cell row cell 1 over 3600 end cell row cell 1 over 6000 end cell end table close square brackets
rightwards double arrow straight x equals 2400 comma space straight y space equals space 3600 space and space straight z equals 6000 end style

Answered by Rebecca Fernandes | 11th Sep, 2016, 06:52: PM