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Which of the following statements are true? Remember that a mathematical statement is said to be true if it is always true, under all circumstances. b is consistent if the augmented A. The equation Ax matrix [A | b] has a pivot position in every row. B. The solution set of a linear system whose augmented matrix is a1 a2 az b] is the same as the solution set of Ax = b, if A = [a1 a2 az]. OC. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x. ND. If A is an m x n matrix whose columns do not span R", then the equation Ax = b is inconsistent for some b in Rm. E. The equation Ax = b is referred to as equation. vector F. 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.

Which of the following statements are true? Remember that a mathematical statement is said to be true if it is always true, under all circumstances. b is consistent if the augmented A. The equation Ax matrix [A | b] has a pivot position in every row. B. The solution set of a linear system whose augmented matrix is a1 a2 az b] is the same as the solution set of Ax = b, if A = [a1 a2 az]. OC. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x. ND. If A is an m x n matrix whose columns do not span R", then the equation Ax = b is inconsistent for some b in Rm. E. The equation Ax = b is referred to as equation. vector F. 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.

Advanced Engineering Mathematics
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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Which of the following statements are true? Remember that a mathematical statement is said to be true if it is always true, under all circumstances. A. The equation Ax = b is consistent if the augmented matrix A| 6| has a pivot position in every row. B. The solution set of a linear system whose augmented matrix is a1 a2 az | b| is the same as the solution set of Ax = b, if A = [a1 a2 a3 ]. |C. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x. |D. If A is an m × n matrix whose columns do not span R", then the equation Ax b in Rm. b is inconsistent for some E. The equation Ax = b is referred to as a vector equation. F. 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.
Transcribed Image Text:Which of the following statements are true? Remember that a mathematical statement is said to be true if it is always true, under all circumstances. A. The equation Ax = b is consistent if the augmented matrix A| 6| has a pivot position in every row. B. The solution set of a linear system whose augmented matrix is a1 a2 az | b| is the same as the solution set of Ax = b, if A = [a1 a2 a3 ]. |C. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x. |D. If A is an m × n matrix whose columns do not span R", then the equation Ax b in Rm. b is inconsistent for some E. The equation Ax = b is referred to as a vector equation. F. 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.
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