Determine whether each statement below is true or false. Justify each answer. a. The equation Ax =b is referred to as a vector equation. Choose the correct answer below.
A. True The equation Ax b is referred to as a vector equation because A is constructed from column vectors
B. False. The equation Ax= b is referred to as a matrix equation because A is a matrix
C. True. The equation Ax- b is referred to as a vector equation because it consists of scalars multiplied by vectors ○
D. False. The equation Ax-b is referred to as a linear equation because b is a linear combination of vectors.
b. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax b has at least one solution. Choose the correct answer below.
A. False. If the equation Ax-b has infinitely many solutions, then the vector b cannot be a linear combination of the columns of A
B. True The equation Ax-b is unrelated to whether the vector b is a linear combination of the columns of a matrix A. °
C. False. If the matrix A is the identity matrix, then the equation Ax: b has at least one solution, but b is not a linear combination of the columns of A.
D. True. The equation Ax-b has the same solution set as the equation x1a1 + x2a2 +···+xnan-b
c. The equation Ax b is consistent if the augmented matrix A b has a pivot position in every row. Choose the correct answer below.
A. False. The augmented matrix [ A b cannot have a pivot position in every row because it has more columns than rows
B. False. If the augmented matrix「A b has a pivot position in every row, the equation equation Ax-b may or may not be consistent. One pivot position may be in the column representing b Click to select your answer.