GATE MA 2024 Paper 1 — page 7

Questions 19–21 of 65. Imported answers require review unless explicitly marked reviewed.

Let

and

be the linear transformation given by

. The characteristic polynomial of

Your answerChoose one option.

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Let

be a normal matrix. Consider the following statements.

I. If all the eigenvalues of

are real, then

is Hermitian.

II. If all the eigenvalues of

have absolute value 1, then

is unitary.

Which one of the following is correct?

Your answerChoose one option.

Both I and II are TRUE

I is TRUE and II is FALSE

I is FALSE and II is TRUE

Both I and II are FALSE

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Let

and

be a

real column vector. Consider the statements.

I. The Jacobi iteration method for the system

converges for any initial approximation and

II. The Gauss–Seidel iteration method for the system

converges for any initial approximation and

Which one of the following is correct?

Your answerChoose one option.

Both I and II are TRUE

I is TRUE and II is FALSE

I is FALSE and II is TRUE

Both I and II are FALSE

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2024 · Paper 1