For the matrix [A] = \left[\begin{array}{ccc}1 & −1 & 0 \ \text{ −1} & 2 & −1 \ \text{ 0} & −1 & 1 \ ]\end{array} which of the following statements is/are TRUE?

[𝐴]{𝑥} = {𝑏} has a unique solution

[𝐴]{𝑥} = {𝑏} does not have a unique solution

[𝐴] has three linearly independent eigenvectors

[𝐴] is a positive definite matrix

GATE Civil Engineering (CE) 2023 Shift 2 Solved Paper

Question : 26 of 65

Marks: +1, -0

For the matrix

[A] = {[\table 1 , −1 , 0 ; \text" −1" , 2 , −1 ; \text" 0" , −1 , 1 ; ]}

which of the following statements is/are TRUE?

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