Question
Download Solution PDFThe system of linear equations
-y + z = 0
(4d - 1) x + y + Z = 0
(4d - 1) z = 0
has a non-trivial solution, if d equals
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
For a homogeneous system of linear equations:
Having non-trivial solution:
The rank of the matrix should be less than the number of variables.
Or determinant of the matrix should be equal to zero.
Calculation:
Given:
-y + z = 0
(4d - 1) x + y + Z = 0
(4d - 1) z = 0
So, A =
For non-trivial solution:
det. A = 0
⇒
⇒ 0 × [(4d - 1) - 0] + 1 × [(4d - 1)2 - 0] + 1(0 - 0) = 0
⇒ (4d - 1)2 = 0
⇒ d =
∴ The system of linear equations has a non-trivial solution if d equals to
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