Engineering Maths - Linear Algebra

6. In the matrix equation Px = q. which of the following is a necessary condition for the existence of at least one solution for the unknown vector x?

  • Option : A
  • Explanation : According to Rouche's theorem, the system is consistent if and only if the coefficient matrix and the augmented matrix K are of the same rank, otherwise the system is inconsistent.
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7. Rank of the diagonal matrix Rank of the diagonal matrix

  • Option : D
  • Explanation : Since the number of non-zero elements on this diagonal matrix is four, hence the rank is four.
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8. Matrix, A =

 
cosΘ sinΘ 0
sinΘ cosΘ 0
0 0 1
 

  • Option : D
  • Explanation : Determinant A = 1 (cos2Θ + sin2Θ) Hence A is non-singular and A-1 exists
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