The maximum value of “$a$” such that the matrix $\left( {\begin{array}{*{20}{c}} { - 3}&0&{ - 2}\ 1&{ - 1}&0\ 0&a&{ - 2} \end{array}} \right)$ has three linear independent real eigenvectors is

Question

The maximum value of “$a$” such that the matrix $\left( {\begin{array}{*{20}{c}} { - 3}&0&{ - 2}\ 1&{ - 1}&0\ 0&a&{ - 2} \end{array}} \right)$ has three linear independent real eigenvectors is

TuteeHUB · Accepted Answer

$\frac{{1 + 2\sqrt 3 }}{{3\sqrt 3 }}$

TuteeHUB · Answer

$\frac{2}{{3\sqrt 3 }}$

TuteeHUB · Answer

$\frac{1}{{3\sqrt 3 }}$

TuteeHUB · Answer

$\frac{{1 + \sqrt 3 }}{{3\sqrt 3 }}$

1.	The maximum value of “\(a\)” such that the matrix \(\left( {\begin{array}{*{20}{c}} { - 3}&0&{ - 2}\\ 1&{ - 1}&0\\ 0&a&{ - 2} \end{array}} \right)\) has three linear independent real eigenvectors is
A.	\(\frac{2}{{3\sqrt 3 }}\)
B.	\(\frac{1}{{3\sqrt 3 }}\)
C.	\(\frac{{1 + 2\sqrt 3 }}{{3\sqrt 3 }}\)
D.	\(\frac{{1 + \sqrt 3 }}{{3\sqrt 3 }}\)
Answer» C. \(\frac{{1 + 2\sqrt 3 }}{{3\sqrt 3 }}\)

The maximum value of “\(a\)” such that the matrix \(\left( {\begin{array}{*{20}{c}} { - 3}&0&{ - 2}\\ 1&{ - 1}&0\\ 0&a&{ - 2} \end{array}} \right)\) has three linear independent real eigenvectors is

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