Consider the matrix \left[\begin{array}{cc}5 & −1 \ 4 & 1 \ ]\end{array} which one of the following statements is TRUE for the eigenvalues and eigenvectors of the matrix?

Correct Answer is : Eigen value 3 has a multiplicity of 2 and only one independent eigen vector exists

Eigen value 3 has a multiplicity of 2 and only one independent eigen vector exists

Eigen value 3 has a multiplicity of 2 and two independent eigen vectors exist

Eigen value 3 has a multiplicity of 2 and no independent eigen vector exists

Eigen values are 3 and –3 and two independent eigen vectors exist.

GATE Civil Engineering (CE) 2017 Shift 1 Solved Paper

Question : 38 of 65

Marks: +1, -0

Consider the matrix

{[\table 5 , −1 ; 4 , 1 ; ]}

which one of the following statements is TRUE for the eigenvalues and eigenvectors of the matrix?

Eigen value 3 has a multiplicity of 2 and only one independent eigen vector exists
Eigen value 3 has a multiplicity of 2 and two independent eigen vectors exist
Eigen value 3 has a multiplicity of 2 and no independent eigen vector exists
Eigen values are 3 and –3 and two independent eigen vectors exist.

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