BUSINESS ADMINISTRATION
BUSINESS MATHEMATICS
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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p(A) = p(A, B) > n
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p(A) =p (A, B) =n
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all the above
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none of these
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Detailed explanation-1: -Solution of Non-homogeneous system of linear equations Matrix method: If AX = B, then X = A-1B gives a unique solution, provided A is non-singular. But if A is a singular matrix i.e., if |A| = 0, then the system of equation AX = B may be consistent with infinitely many solutions or it may be inconsistent.
Detailed explanation-2: -Since, by the rank theorem, rank(A) + dim(N(A)) = n (recall that n is the number of columns of A), the system AX = B has a unique solution if and only if rank(A) = n. A linear system of the form AX = 0 is said to be homogeneous. Solutions of AX = 0 are vectors in the null space of A.
Detailed explanation-3: -A system of linear equations, written in the matrix form as AX = B, is consistent if and only if the rank of the coefficient matrix is equal to the rank of the augmented matrix; that is, ( A) = ([ A | B]).
Detailed explanation-4: -The system AX=B of non-homogeneous linear equations is consistent if and only if rank A=rank [AB]-YouTube.