a. Every matrix equation Ax b corresponds to a vector equation with the same sol

Question

a. Every matrix equation Ax b corresponds to a vector equation with the same solution set. Choose the correct answer below. O A. False. The matrix equation Ax-b does not correspond to a vector equation with the same solution set. O B. False. The matrix equation Ax b only corresponds to an inconsistent system of vector equations. O c. True. The matrix equation Ax-bis simply another notation for the vector equation x1a1 + x2a2 +·.. + xnan-b, where al , O D. True. The matrix equation Ax-bis simply another notation for the vector equation x1a1 + x2a2 +·.. + xna,-b, where al , , an are the columns of A , an are the rows of A b. If the equation Ax = b is consistent, then b is in the set spanned by the columns of A. Choose the correct answer below. O A. True. The equation Ax b has a solution set if and only if A has a pivot position in every row. O B. True. The equation Ax b has a nonempty solution set if and only if b is a linear combination of the columns of A. ? c. False, b is only included in the set spanned by the columns of A if Ax-bis inconsistent. O D. False. Ax b is only consistent if the values of b are nonzero c. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x. Choose the correct answer below. O A. True. Ax can be written as a linear combination of vectors because any two vectors can be combined by addition O B. False. A and x cannot be written as a linear combination because the matrices do not have the same dimensions. ° C. True. The matrix A is the matrix of coefficients of the system of vectors. O D. False. A and x can only be written as a linear combination of vectors if and only if in Ax b, b is nonzero.

Explanation / Answer

a) Option C is correct.

b) Option A is correct.

c) Option C is correct.

d) Option B is correct.

e) Option A is correct.

f) Option A is correct.

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