GATE CE area:engineering-mathematics PYQs & Answers — Page 18

Questions 171–174 of 174. Imported answers require independent review unless marked reviewed.

Topic practice 174 questionsPage 18 of 18

Consider the matrix

. Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?

Your answerChoose one option.

Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.

Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.

Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.

Eigenvalues are 3 and -3, and two independent eigenvectors exist.

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and

is equal to

Your answerChoose one option.

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Consider the following second-order differential equation:

The particular solution of the differential equation is

Your answerChoose one option.

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Consider the equation

with

. This is numerically solved by using the forward Euler method with a step size,

. The absolute error in the solution at the end of the first time step is

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GATE CE area:engineering-mathematics PYQs