If the det (M) ≠0 then A. some values of X will have no values of A which satisfy the equation. B. some values of X will have more than one value of A which satisfy the equation. C. given any A there is one and only one X which will satisfy the equation. D. some values of A (such as A=0) will allow more than one X to satisfy the equation. E. given any X there is one and only one A which will satisfy the equation. F. some values of A will have no values of X which will satisfy the equation.

Question

Mathematics

Axle

12 December, 15:29

If the det (M) ≠0 then A. some values of X will have no values of A which satisfy the equation. B. some values of X will have more than one value of A which satisfy the equation. C. given any A there is one and only one X which will satisfy the equation. D. some values of A (such as A=0) will allow more than one X to satisfy the equation. E. given any X there is one and only one A which will satisfy the equation. F. some values of A will have no values of X which will satisfy the equation.

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Alyvia Jefferson · Answer 1

C. given any A there is one and only one X which will satisfy the equation.

D. some values of A (such as A=0) will allow more than one X to satisfy the equation.

Step-by-step explanation:

If the value of the determinant is not equal to zero then the number of the solution depends on the rank of the augmented matrix (M), the rank of matrix A and the number of unknowns. Thus, the number of solutions of the matrix can be infinitely many solutions, a single solution or no solution.