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  • Stuck here, help me understand: - Matrices and Determinants - JEE Main

If the system of linear equations


x+ky+3z=0

3x+ky-2z=0

2x+4y-3z=0
has a non-zero solution (x, y, z), then \frac{xz}{y^{2}}
is equal to :

  • Option 1)

    30

  • Option 2)

    -10

  • Option 3)

    10

  • Option 4)

    -30

 

Answers (2)

We can see D_{1}= D_{2}= D_{3}= 0

\begin{bmatrix} 1 & k&-3 \\ 3& k& -2\\ 2&4 & -3 \end{bmatrix}

on  solving x = -5y 

z= -2y 

\frac{xz}{y^{2}}=10

 

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

 

 


Option 1)

30

Option 2)

-10

Option 3)

10

Option 4)

-30

Posted by

subam

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