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Which of the following statements are true? A. If the linear system whose augmented matrix is [A₁ A₂ A3 | b] has a unique solution, then the matrix A =[A₁ A₂ A3 ] is nonsingular. B. The matrix A is singular if the augmented matrix [ A | b ] has a pivot position in every row. C. If A is a singular n x n matrix, then A cannot have a pivot position in every row. D. If the equation Ax = b does not have a solution, then the matrix A is singular. E. Any linear combination of n-vectors in R" can always be written in the form Ax for a suitable matrix A and vector x. F. The equation Ax = h has a unique solution if and only if the matrix A is singular.

Which of the following statements are true? A. If the linear system whose augmented matrix is [A₁ A₂ A3 | b] has a unique solution, then the matrix A =[A₁ A₂ A3 ] is nonsingular. B. The matrix A is singular if the augmented matrix [ A | b ] has a pivot position in every row. C. If A is a singular n x n matrix, then A cannot have a pivot position in every row. D. If the equation Ax = b does not have a solution, then the matrix A is singular. E. Any linear combination of n-vectors in R" can always be written in the form Ax for a suitable matrix A and vector x. F. The equation Ax = h has a unique solution if and only if the matrix A is singular.

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? A. If the linear system whose augmented matrix is [A₁ A2 A3 | b ] has a unique solution, then the matrix A =[A₁ A₂ A3 ] is nonsingular. B. The matrix A is singular if the augmented matrix [ A | b ] has a pivot position in every row. C. If A is a singular n × n matrix, then A cannot have a pivot position in every row. D. If the equation Ax=b does not have a solution, then the matrix A is singular. E. Any linear combination of n-vectors in R" can always be written in the form Ax for a suitable matrix A and vector x. F. The equation Ax = b has a unique solution if and only if the matrix A is singular.
Transcribed Image Text:Which of the following statements are true? A. If the linear system whose augmented matrix is [A₁ A2 A3 | b ] has a unique solution, then the matrix A =[A₁ A₂ A3 ] is nonsingular. B. The matrix A is singular if the augmented matrix [ A | b ] has a pivot position in every row. C. If A is a singular n × n matrix, then A cannot have a pivot position in every row. D. If the equation Ax=b does not have a solution, then the matrix A is singular. E. Any linear combination of n-vectors in R" can always be written in the form Ax for a suitable matrix A and vector x. F. The equation Ax = b has a unique solution if and only if the matrix A is singular.
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