4. Our definition of an invertible matrix requires that A be a square n x n matrix. Let's examine what happens when A is not square. For instance, suppose that -1 -2 1 A = -2 -1 B = 1 -2 -1 3 a. Verify that BA = I2. In this case, we say that B is a left inverse of A. b. If A has a left inverse B, we can still use it to find solutions to linear equations. If we know there is a solution to the equation Ax = b, we can multiply both sides of the equation by B to find x = Bb. Suppose you know there is a solution to the equation Ax 3 Use 6 the left inverse B to find x and verify that it is a solution. С. Now consider the matrix 1 -1 C = -2 1 and verify that C is also a left inverse of A. This shows that the matrix A may have more than one left inverse. d. When A is a square matrix, we said that BA this problem, we have a non-square matrix A with BA = happens when we compute AB? I implies that AB = I. In I. What
4. Our definition of an invertible matrix requires that A be a square n x n matrix. Let's examine what happens when A is not square. For instance, suppose that -1 -2 1 A = -2 -1 B = 1 -2 -1 3 a. Verify that BA = I2. In this case, we say that B is a left inverse of A. b. If A has a left inverse B, we can still use it to find solutions to linear equations. If we know there is a solution to the equation Ax = b, we can multiply both sides of the equation by B to find x = Bb. Suppose you know there is a solution to the equation Ax 3 Use 6 the left inverse B to find x and verify that it is a solution. С. Now consider the matrix 1 -1 C = -2 1 and verify that C is also a left inverse of A. This shows that the matrix A may have more than one left inverse. d. When A is a square matrix, we said that BA this problem, we have a non-square matrix A with BA = happens when we compute AB? I implies that AB = I. In I. What
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 5AEXP
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage