Determine whether each of statements a through f below are true or false. Justif

Question

Determine whether each of statements a through f below are true or false. Justify each answer. a. Every matrix equation Ax b corresponds to a vector equation with the same solution set. Choose the correct answer below. O A. True. The matrix equation Ax-bis simply another notation for the vector equation x1a1 +x2a2 +···+xnan-b, where a 1 O B. False. The matrix equation Ax b only corresponds to an inconsistent system of vector equations. O c. False The matrix equation Ax = b does not correspond to a vector equation with the same solution set 0 D. True. The matrix equation Ax-b is simply another notation for the vector equation x1a1 + x2a2 +···+xnan-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. 0 A. O B. ° C. False. Ax= b is only consistent if the values of b are nonzero False, b is only included in the set spanned by the columns of A if Ax= b is inconsistent. True. The equation Ax = b has a nonempty solution set if and only if b is a linear combination of the columns of A. D. True. The equation Ax= b has a solution set if and only if A has a pivot position in every row. 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. The matrix A is the matrix of coefficients of the system of vectors. O B. False. A and x can only be written as a linear combination of vectors if and only if in Ax= b, b is nonzero. O C. False. A and x cannot be written as a linear combination because the matrices do not have the same dimensions. Click to select your answer.

Explanation / Answer

1. answer d

explanation: the matrix is written by using the vector equations and each vector equation is one row of the matrix 1 the solution set of the matrix is depend on the coefficents of the vectors and the vector equations is doesn't change in the system before completing the solution the system

2 answer a

explanation : if the matrix is consistency means that the equations has a only one solution and that solution is not zero solution i.e,the set of x is not becomes zero and the row echelon form of the matrix a is a ideal matrix then the values of the matrix b is a solution of the matrix a the values in the matrix a except diagonal elements is becomes zero

3 answer 1

the matirx is written by using the coefficients in the vector equations

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