Question

If R(A)≠r[A;b]then the system is =---------
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Answer 1

Answer:- (Step By Step)

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

Rank method for solution of Non-Homogeneous system AX = B

Write down A, B

Write the augmented matrix [A : B]

Reduce the augmented matrix to Echelon form by using elementary row operations.

Find the number of non-zero rows in A and [A : B] to find the ranks of A and [A : B] respectively.

If ρ(A) ≠ ρ(A : B) then the system is inconsistent.

ρ(A) = ρ(A : B) = the number of unknowns, then the system has a unique solution.

ρ(A) = ρ(A : B) < number of unknowns, then the system has an infinite number of solutions.

Necessary:-

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Answer 2

Answer:

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