Mathematics - Vectors and Matrices

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26. Given: matrix A=

The eigen vector corresponding to the smallest eigen value is

Given: matrix A=The eigen vector corresponding to the smallest eigen value is

  • Option : A
  • Explanation : For finding eigen vector corresponding to 1, 

    putting λ equal to 1. 

    Linear Algebra

    Rank of the coefficient matrix=

    = Number of non-zero diagonal elements

    = 2 < 3.

    Hence non-zero solution vector = 3 - 2 = 1 

    Linear Algebra

    These equation can be rewritten as

    Linear Algebra

    From these equations,

    Linear Algebra

    Linear Algebra

      Hence is the required eigen vector.

    Linear Algebra

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27. Rank the following (n+1)×(n+1)matrix, where a is a real number, is Rank the following (n+1)×(n+1)matrix, where a is a real number, is

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28. Matrices 

Matrices

commute under multiplication

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29. Eigen values of the system represented by

X=
 
0100
0010
0001
0001
 
Xare

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30. The rank of  the matrix  is

     
 
11
00
 
 

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