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+2 votes
24.5k views
in Matrices & determinants by (41.3k points)

Discuss for all values of l, the system of equations x + y + 4z = 6, x + 2y -2z = 6, xλ + y + z = 6 with regards to existence and nature of solutions.

1 Answer

+2 votes
by (41.5k points)
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Best answer

The matrix form of the given system is

The given system of equations will have a unique solution iff the coefficient matrix is non-singular. Using R2 → R2 - R1, R3 → R3λR1, we get

Therefore, the coefficient matrix will be non-singular if

1 - 4λ + 6 - 6λ ≠ 0 ⇒ λ ≠ 7 10

Thus, the given system will have a unique solution if λ ≠ 7/10. 

In case λ = 7/10 , Eq. (1) becomes

This shows that the equations are not consistent in this case. 

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