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Engineering Maths MCQ - 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?

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.

7 Rank of the diagonal matrix

Since the number of non-zero elements on this diagonal matrix is four, hence the rank is four.

8 Matrix, A =

cosΘ	sinΘ	0
sinΘ	cosΘ	0
0	0	1

Determinant A = 1 (cos2Θ + sin2Θ) Hence A is non-singular and A^-1exists

9 The matrix B = A^T, where A is any matrix is

10 Eigen values of a real symmetric matrix are always

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Rank of the matrix 0 0 -3 9 3 5 3 1 1

A. 0
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C. 2
D. -1

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Engineering Maths MCQ - Linear Algebra

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