Concept explainers
True or false? If det(A) = 0, then A is not invertible.
To state: Whether the given statement is true or false.
Answer to Problem 3E
The statement that if
Explanation of Solution
If determinant of a matrix is zero, the system of equations associated with it is linearly dependent. At least one row of such a matrix is a scalar multiple of another.
If the determinant of a matrix is nonzero, linear system it represents is linearly independent and its rows are linearly dependent vectors, and its columns are linearly dependent vectors.
As from above statements it is clear that determinant holds true for dependency of systems.
Thus, from the above statements the statement that if
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning