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  • Need explanation for: - If the system of linear equations is consistent, then : - Matrices and Determinants - JEE Main

If the system of linear equations 

x-4y+7z=g

3y-5z=h

-2x+5y-9z=k

is consistent, then :

  • Option 1)

     

    g+h+k=0

  • Option 2)

     

     

    g+h+2k=0

  • Option 3)

     

    g+2h+k=0

  • Option 4)

     

    2g+h+k=0

Answers (1)

best_answer

 

Solution of a non-homogeneous system of linear equations by matrix method -

If A is a singular matrix and Adj(A).b\neq 0, then the system of equations given by Ax=b has no solution

- wherein

 

 

Consistent system of linear equation -

If the system of equations has one or more solutions 

-

 

Given that the system of linear equation.

Let

\\P_1 = x-4y+7z-g=0 \\P_2 = 3x - 5y - h= 0 \\P_3 = -2x+5y-9z-k = 0

Here \Delta = 0

2P_1 + P_2 + P_3 = 0  when  2g + h + k = 0


Option 1)

 

g+h+k=0

Option 2)

 

 

g+h+2k=0

Option 3)

 

g+2h+k=0

Option 4)

 

2g+h+k=0
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