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Engineering Maths · Q134

Linear Algebra

Engineering and GATE · Engineering Maths · question 134

Q134

The matrix \[ M = [ array*20c - 2&2& - 3 \\ 2&1& - 6 \\ - 1& - 2&0 array ]\] has eigen values -3, -3, 5. An eigen vector corresponding to the eigen value 5 is [1 2 -1]T. One of the eigen vectors of the matrix M3 is

The matrix {\text{M}} = \left[ {\begin{array}{*{20}{c}} { - 2}&2&{ - 3} \\ 2&1&{ - 6} \\ { - 1}&{ - 2}&0 \end{array}} \right]    has eigen values -3, -3, 5. An eigen vector corresponding to the eigen value 5 is [1 2 -1]T. One of the eigen vectors of the matrix M3 is
A.
[1 8 -1]T
B.
[1 2 -1]T
Answer
C.
{\left[ {\begin{array}{*{20}{c}} 1&{\sqrt[3]{2}}&{ - 1} \end{array}} \right]^{\text{T}}}
D.
[1 1 -1]T

Answer: Option B

Solution

Answer: Option B
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