To find:the inverse of the matrix
Answer to Problem 20E
The inverse of the matrix is
Explanation of Solution
Given information:
Concept Involved:
Definition of Matrix Multiplication:
If
The definition of matrix multiplication uses a row-by-column multiplication, where the entry in the
So, for the product of two matrices to be defined, the number of columns of the first matrix must equal the number of rows of the second matrix. That is, the middletwo indices must be the same.
The outside two indices give the dimension of the product as show below
Definition of the Inverse of a Square Matrix:
Let A be
To show that B is the inverse of A, we need to show that AB = I = BA.
Finding an Inverse Matrix:
Let A be a square matrix of dimension n × n.
1. Write the
2. If possible, row reduce A to I using elementary row operations on the entirematrix
3. Check your work by multiplying to see that
Calculation:
Begin by adjoining the identity matrix to A to form the matrix
Use elementary row operations to obtain the form
- Add -3 times the 1st row to the 2nd row
- Add 1 times the 1st row to the 3rd row
- Add 2 times the 2nd row to the 3rd row
- Add -3 times the 3rd row to the 2nd row
- Add -2 times the 3rd row to the 1st row
- Add -2 times the 2nd row to the 1st row
Conclusion:
The inverse of the matrix
Chapter 8 Solutions
EBK PRECALCULUS W/LIMITS
- 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