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# I need help with - Matrices and Determinants - JEE Main-3

Consider the system of equation

x + 2y - z = 6

2x + 3y + z = 3

3x + 5y + $\lambda$z = $\mu$ then system has

• Option 1)

Infinite solutions, if  $\lambda$ = 0, $\mu$ = 9

• Option 2)

No solution, if $\lambda$ $\neq$ 0, $\mu$ = 9

• Option 3)

Unique solution, if $\lambda$ $\neq$ 0, $\mu$ $\neq$  9

• Option 4)

All of these

Answers (1)
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As we have learned

Inconsistent system of linear equation -

If the system of equations has no solutions

-

If $\lambda$ = 0, then 3rd equation is I + II, so, for infinite solutions $\mu$ = 6 + 3

Similarly other cases.

Option 1)

Infinite solutions, if  $\lambda$ = 0, $\mu$ = 9

Option 2)

No solution, if $\lambda$ $\neq$ 0, $\mu$ = 9

Option 3)

Unique solution, if $\lambda$ $\neq$ 0, $\mu$ $\neq$  9

Option 4)

All of these

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