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Solved: a. The equation Ax = b is referred to as a vector
Chapter 1, Problem 23E(choose chapter or problem)
PROBLEM 23E
a. The equation Ax = b is referred to as a vector equation.
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.
c. The equation Ax = b is consistent if the augmented matrix [A b] has a pivot position in every row.
d. The first entry in the product Ax is a sum of products.
e. If the columns of an m × n matrix A span ℝm, then the equation Ax = b is consistent for each b in ℝm.
f. If A is an m × n matrix and if the equation Ax = b is inconsistent for some b in ℝm, then A cannot have a pivot position in every row.
Questions & Answers
QUESTION:
PROBLEM 23E
a. The equation Ax = b is referred to as a vector equation.
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.
c. The equation Ax = b is consistent if the augmented matrix [A b] has a pivot position in every row.
d. The first entry in the product Ax is a sum of products.
e. If the columns of an m × n matrix A span ℝm, then the equation Ax = b is consistent for each b in ℝm.
f. If A is an m × n matrix and if the equation Ax = b is inconsistent for some b in ℝm, then A cannot have a pivot position in every row.
ANSWER:
Solution
Step 1:
(a)The equation Ax = b is referred to as a vector equation.
False.the vector equation is of the form ,where
are the columns of A and x is in
The equation is matrix equation.