Exams Joint Entrance Examination Mathematics Matrices and Determinants Question 371 Question 371 of 472 Medium MCQ
The values of \[\lambda \] and \[\mu \] for which the system of linear equations
x + y + z = 2
x + 2y + 3z = 5
x + 3y + \[\lambda \]z = \[\mu \]
has infinitely many solutions are, respectively:
Solutions · 1 Post your solution Official solution
For infinite many solutions
D = D1 = D2 = D3 = 0
Now D = \[\left| { ( 1 1 1 1 2 3 1 3 λ ) \begin{pmatrix} 1 & 1 & 1 \\
1 & 2 & 3 \\
1 & 3 & \lambda \\
\end{pmatrix} 1 1 1 1 2 3 1 3 λ } \right|\] = 0
\[ \Rightarrow \] 1. (2\[\lambda \] -- 9) --1.(\[\lambda \] -- 3) + 1.(3 -- 2) = 0
\[ \Rightarrow \] \[\lambda \] = 5
Now D1 = \[\left| { ( 2 1 1 5 2 3 μ 3 5 ) \begin{pmatrix} 2 & 1 & 1 \\
5 & 2 & 3 \\
\mu & 3 & 5 \\
\end{pmatrix} 2 5 μ 1 2 3 1 3 5 } \right|\] = 0
\[ \Rightarrow \] 2(10 -- 9) --1(25 -- 3\[\mu \]) + 1(15 -- 2\[\mu \]) = 0
\[ \Rightarrow \] \[\mu \] = 8 Answer the question to unlock