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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?
Augmented matrix [Pq] must have the same rank as matrix P
Vector q must have only non-zero elements
Matrix P must be singular
None of these
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7. Rank of the diagonal matrix
1
2
3
4
8. Matrix, A =
orthogonal
non-singular
have A-1 exists
both (b) & (c)
9. The matrix B = AT, where A is any matrix is
skew symmetric
symmetric about the secondary diagonal
always symmetric
another general matrix
10. Eigen values of a real symmetric matrix are always
positive
real and imaginary
negative
real
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