(a) To determine:
Guess which
Given information:
Determinant
Concept used:
The
Calculation:
Let us consider the following matrices
According to Cauchy-Binet formula:
Conclusion:
(b) To Check:
Test your formula when the rows of
Given information:
Concept used:
The 2 by 2 matrix AB = (2 by 3)(3 by 2) has a "Cauchy-Binet formula" for det AB.
Calculation:
The
Let us check the above statements with an example.
According to Cauchy-Benet formula,
Now again find the determinant of
Conclusion:
Thus, the
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Introduction to Linear Algebra, Fifth Edition
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education