GATE MA 2017 Paper 1 — page 9

Questions 25–27 of 65. Imported answers require review unless explicitly marked reviewed.

For a linear programming problem (LP) and its dual, which one of the following is NOT TRUE?

Your answerChoose one option.

The dual of the dual is primal

If the primal LPP has an unbounded objective function, then the dual LPP is infeasible

If the primal LPP is infeasible, then the dual LPP must have unbounded objective function

If the primal LPP has a finite optimal solution, then the dual LPP also has a finite optimal solution

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and

are the null spaces of

and

, respectively, then the dimension of the subspace

equals ________.

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Given two

matrices

and

with entries in

, consider the following statements: (P): If

and

have the same minimal polynomial, then

is similar to

. (Q): If

has

distinct eigenvalues, then there exists

such that

are linearly independent. Which of the above statements hold TRUE?

Your answerChoose one option.

Both P and Q

Only P

Only Q

Neither P nor Q

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2017 · Paper 1