QJEEAdv08Ma81c2: JEE Advanced 2008 Mathematics - Class 12 JEEAdv08Ma81c2 Solution: Consider the system of equations: x − 2 y + 3 z = − 1 − x + y − …

Question

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Consider the system of equations:

$x - 2 y + 3 z = - 1$

$- x + y - 2 z = k$

$x - 3 y + 4 z = 1$

Statement - 1 : The system of equations has no solution for $k \neq 3$ .

and

Statement - 2 : The determinant $| \begin{matrix} 1 & 3 & - 1 \\ - 1 & - 2 & k \\ 1 & 4 & 1 \end{matrix} | \neq 0$ , for $k \neq 3$ .

A Statement - 1 is True, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1
B Statement - 1 is True, Statement - 2 is True; Statement - 2 is NOT a correct explanation for Statement - 1
C Statement - 1 is True, Statement - 2 is False
D Statement - 1 is False, Statement - 2 is True

Accepted Answer

The given equations are

$x - 2 y + 3 z = - 1$

$- x + y - 2 z = k$

$x - 3 y + 4 z = 1$

$D = | \begin{matrix} 1 & - 2 & 3 \\ - 1 & 1 & - 2 \\ 1 & - 3 & 4 \end{matrix} | = 0$

$D = | \begin{matrix} 1 & - 1 & 3 \\ - 1 & k & - 2 \\ 1 & 1 & 4 \end{matrix} | = k - 3 \neq 0$

If $k \neq 3$ , the system has no solutions.

Hence, Statement - 1 is True Statement - 2 is correct explanation for Statement - 1.

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