Exams Joint Entrance Examination Mathematics Matrices and Determinants Question 418 Question 418 of 472 Medium MCQ
If the system of linear equations
2x + y - z = 7
x - 3y + 2z = 1
x + 4y + \[\delta\]z = k, where \[\delta\], k \[\in\] R has infinitely many solutions, then \[\delta\] + k is equal to:
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2 x + y − z = 7 2x + y - z = 7 2 x + y − z = 7
x − 3 y + 2 z = 1 x - 3y + 2z = 1 x − 3 y + 2 z = 1
\[x + 4y + \delta z = k\]
\[\Delta = \left| { ( 2 1 − 1 1 − 3 2 1 4 δ ) \begin{pmatrix} 2 & 1 & { - 1} \\
1 & { - 3} & 2 \\
1 & 4 & \delta \\
\end{pmatrix} 2 1 1 1 − 3 4 − 1 2 δ } \right| = - 7\delta - 21 = 0\]
\[\delta = - 3\]
\[{\Delta _1} = \left| { ( 7 1 − 1 1 − 3 2 k 4 − 3 ) \begin{pmatrix} 7 & 1 & { - 1} \\
1 & { - 3} & 2 \\
k & 4 & { - 3} \\
\end{pmatrix} 7 1 k 1 − 3 4 − 1 2 − 3 } \right|\]
\[ \Rightarrow 6 - k = 0 \Rightarrow k = 6\]
\[\delta + k = - 3 + 6 = 3\] Answer the question to unlock