Engineering math's CS

Engineering math's CS
Question:-
Option (A)
consistent having a unique solution
Option (B)
consistent having many solutions
Option (C)
inconsistent having a unique solution
Option (D)
inconsistent having no solution
Correct Option:
C
Question Solution:
    In an over determined system having more equations than variables, all three possibilities still exist (a) consistent unique (b) consistent infinite and (d) in consistent with no situation such a system will not be in consistent having a unique solution.
Question:-
Option (A)
3    1    4    2
Option (B)
2    3    4    1
Option (C)
3    2    5    4
Option (D)
3    4    2    1
Correct Option:
A
Question Solution:
    A. Singular matrix -> Determinant is zero
    B. Non-square matrix -> Determinant is not defined
    C. Real symmetric -> Eigen values are always real
    D. Orthogonal matrix -> Determinant is always one
Question:-
Option (A)
2/3
Option (B)
1
Option (C)
3/2
Option (D)
Correct Option:
A
Question Solution:
    
    Let    &θ = (2/3)x
    Required limit =
Question:-
Option (A)
(2 x 2)
Option (B)
(3 x 3)
Option (C)
(4 x 3)
Option (D)
(3 x 4)
Correct Option:
A
Question Solution:
    With the given order we can say that order of matrices are as follows:
    XT    ->    3 x 4
    Y    ->    4 x 3
    XTY    ->    3 x 3
    (XTY)-1    3 x 3
    P    ->    2 x 3
    PT     ->    3 x 2
    P(XTY)-1PT    ->    (2 x 3) (3 x 3) (3 x 2) -> 2 x 2
    therefore, (P(XTY)-1PT)T    ->    2 x 2