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The maximum value of “a” such that the matrix 
has three linearly independent real eigenvectors is
has three linearly independent real eigenvectors is- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
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The maximum value of “a” such that the matrix has three linearly in...
The characteristic equation of A is
|A-XI| = 0
⇒ f(x) = x3 + 6x2 + 11x + 6 + 2a
= (x + 1)(x + 2)(x + 3)+2a = 0
f(x) cannot have all 3 real roots (if any) equal
for if f(x) = (x-k)3, then comparing coefficients, we get
6 = –3k, 3k2 = 11
No such k exists
A) Thus f(x) = 0 has repeated (2) roots α, α, β
or
B) f(x) = 0 has real roots (distance) α, β, δ
Now 
At x1, f(x) has relative maximum
At x2, f(x) has relative minimum
The graph of f(x) will be as below
Case A. repeated roots (α, α, β)
Case B. distinct roots
Note that the graph of f(x) cannot be like the one given below
Thus in all possible cares we have
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The maximum value of “a” such that the matrix has three linearly independent real eigenvectors isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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The maximum value of “a” such that the matrix has three linearly independent real eigenvectors isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The maximum value of “a” such that the matrix has three linearly independent real eigenvectors isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum value of “a” such that the matrix has three linearly independent real eigenvectors isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?.
The maximum value of “a” such that the matrix has three linearly independent real eigenvectors isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The maximum value of “a” such that the matrix has three linearly independent real eigenvectors isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum value of “a” such that the matrix has three linearly independent real eigenvectors isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?.
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