(1 point) Consider the following general matrix equation: m11 m12 a2 m21 m22 whi
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Question
(1 point) Consider the following general matrix equation: m11 m12 a2 m21 m22 which can also be abbreviated as By definition, the determinant of M is given by det (M)-mm22 m12m21 The following questions are about the relationship between the determinant of M and the ability to solve the equation above for A in terms of X or for X in terms of A. Check the boxes which make the statement correct If the det (M) 0 then A. given any X there is one and only one A which will satisfy the equation. B. some values of X will have more than one value of A which satisfy the equation C. some values of A (such as A 0) will allow more than one X to satisfy the equation D. given any A there is one and only one X which will satisfy the equation. E. some values of X will have no values of A which satisfy the equation. F. some values of A will have no values of X which will satisfy the equation Check the boxes which make the statement correct If the det (M)-0 then A. given any A there is one and only one X which will satisfy the equation B. some values of A (such as A 0) will allow more than one X to satisfy the equation. C. some values of A will have no values of X which will satisfy the equation D. there is no value of X which satisfies the equation when A 0 E. given any X there is one and only one A which will satisfy the equation Check the conditions that guarantee that det (M)- 0: A. Given any A the is one and only one X which will satisfy the equation. B. There is some value of A for which no value of X satisfies the equation C. When A 0 there is more than one X which satisfies the equation. D. Given any X there is one and only one A which will satisfy the equation.Explanation / Answer
If det(M) is not zero, then
There will be one and only one solution to the equation.
A. is correct option.
If det(M) is zero, then
Either there will be no solution, or there will be infinite solution.
so correct options are B and C.
Conditions for det(M) = 0
A. incorrect. if unique solution exists, det(M) can not be 0
B. Correct. No solution implies det(M) = 0
so answer is B
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