Mathematics - Vectors and Matrices

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61. Inverse of the matrix

Inverse of the matrix

is

  • Option : C
  • Explanation : For the matrix

    Linear Algebra

    cofactors are

    a11= 1, a21 = -5, a12 = -2, a22 = -3

    Therefore matrix by cofactors

    Linear Algebra

    Adjoint A 

    Linear Algebra

    I A I = -3(1) - 5(2)

    = -3 - 10 

    = -13

       Linear Algebra

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62. If A and B are square matrices of size n × n , 

then which of the following statement is not true?

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63. If A be an invertible matrix and inverse of 7A is 

If A be an invertible matrix and inverse of 7A is

then matrix A is

  • Option : A
  • Explanation : Inverse of 7A= 

    Linear Algebra

    Linear Algebra

    = 7 - 8 = -1

    Therefore matrices of co factor

    Linear Algebra

    and its transpose,

      Linear Algebra

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64. If A = 

then state transition matrix eAt is

then state transition matrix eAt is

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65. For the matrix 

one of the eigen values is equal to -2 which of the following is an eigen vector

one of the eigen values is equal to -2.

which of the following is an eigen vector?

  • Option : A
  • Explanation : Linear Algebra

    Putting λ= -2, we get 5x--2y+2z = 0

    Putting  z = 0, we get 5x = 2y

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