Determine whether the statement below is true or false. Justify the answer. 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. O A. This statement is false. If the equation Ax=b has infinitely many solutions, then the vector b cannot be a linear combination of the columns of A. OB. This statement is true. The equation Ax=b is unrelated to whether the vector b is a linear combination of the columns of a matrix A. O C. This statement is true. The equation Ax=b has the same solution set as the equation x₁a₁ + x₂a₂ +---+xª = b. n O D. This statement is 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.
Determine whether the statement below is true or false. Justify the answer. 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. O A. This statement is false. If the equation Ax=b has infinitely many solutions, then the vector b cannot be a linear combination of the columns of A. OB. This statement is true. The equation Ax=b is unrelated to whether the vector b is a linear combination of the columns of a matrix A. O C. This statement is true. The equation Ax=b has the same solution set as the equation x₁a₁ + x₂a₂ +---+xª = b. n O D. This statement is 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer.
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.
O A. This statement is false. If the equation Ax=b has infinitely many solutions, then the vector b cannot be a linear combination of the
columns of A.
O B.
This statement is true. The equation Ax=b is unrelated to whether the vector b is a linear combination of the columns of a matrix
A.
O C. This statement is true. The equation Ax=b has the same solution set as the equation X₁ a₁ + x₂a₂+...+xa = b.
▶
O D. This statement is false. If the matrix A is the identity matrix,
combination of the columns of A.
the equation = b has at least one solution, but b is not a linear
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