With the help of matrices , the solution of the equations  3x+y+2z=3,\, \, 2x-3y-z=-3\, \, x+2y+z=4, is\, \, given\, \, by

  • Option 1)

    x=1, y=2,z=-1

  • Option 2)

    x=-1,y=2,z=1

  • Option 3)

    x=6,y=-2,z=-1

  • Option 4)

    x=-1,y=-2,z=1

 

Answers (1)
P Plabita

As learnt in

Cramer's rule for solving system of linear equations -

When \Delta =0  and \Delta _{1}=\Delta _{2}=\Delta _{3}=0 ,

then  the system of equations has infinite solutions.

- wherein

a_{1}x+b_{1}y+c_{1}z=d_{1}

a_{2}x+b_{2}y+c_{2}z=d_{2}

a_{3}x+b_{3}y+c_{3}z=d_{3}

and 

\Delta =\begin{vmatrix} a_{1} &b_{1} &c_{1} \\ a_{2} & b_{2} &c_{2} \\ a_{3}&b _{3} & c_{3} \end{vmatrix}

\Delta _{1},\Delta _{2},\Delta _{3} are obtained by replacing column 1,2,3 of \Delta by \left ( d_{1},d_{2},d_{3} \right )  column

 

 

We should solve such questions analytically by cross-checking options because of the time constraint.

x=1, y=2,z=-1 , satisfy all these equations


Option 1)

x=1, y=2,z=-1

This option is correct.

Option 2)

x=-1,y=2,z=1

This option is incorrect.

Option 3)

x=6,y=-2,z=-1

This option is incorrect.

Option 4)

x=-1,y=-2,z=1

This option is incorrect.

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