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Mathematics MCQ - Vectors and Matrices

Correct AnswerOption C
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Linear Algebra

A null matrix, when cos 

Linear Algebra

i.e. if 

Linear Algebra

is an odd multiple of 

   Linear Algebra

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Correct AnswerOption A
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Eigen values are given by the solution of equation

Linear Algebra

Since x is real and negative, put x = -k, where k is positive constant

Linear Algebra

Linear Algebra

If λand λ2 be the solutions of the above equations then λand λare eigen values.

Now sum of eigen values = sum of roots of the above equation

Linear Algebra

= 4 (> 0 )

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Correct AnswerOption B
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For given system of equations

Linear Algebra

= 4 (8 - 18) - 6 (7 - 27) + 8 (14 - 24)

= -40 + 120 - 80 = 0

Since  Linear Algebra

= 0, hence given system of equations has unique solution, i.e. only one solution.

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Correct AnswerOption B
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For given system of equations

Linear Algebra

= 4 (8 - 18) - 6 (7 - 27) + 8 (14 - 24)

= -40 + 120 - 80 = 0

Since  Linear Algebra

= 0, hence given system of equations has unique solution, i.e. only one solution.

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Correct AnswerOption C
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Given matrix is 

Linear Algebra

Now

Linear Algebra

Hence eigen values are 0, 0, 3.

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