4. Our definition of an invertible matrix requires that A be a square n x nmatrix. Let's examine what happens when A is not square. For instance,suppose that-1-221A2-1B ==1-2-13a. 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 linearequations. If we know there is a solution to the equation Ax = b, wecan multiply both sides of the equation by B to find x =%3DBb.Suppose you know there is a solution to the equation Ax =-3Usethe left inverse B to find x and verify that it is a solution.C.Now consider the matrix1-1C =-21and verify that C is also a left inverse of A. This shows that the matrix Amay have more than one left inverse.d. When A is a square matrix, we said that BA = I implies that AB = I. Inthis problem, we have a non-square matrix A with BA = I. Whathappens when we compute AB?

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

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

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
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 =
%3D
Bb.
Suppose you know there is a solution to the equation Ax =
-3
Use
the left inverse B to find x and verify that it is a solution.
C.
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 = I implies that AB = I. In
this problem, we have a non-square matrix A with BA = I. What
happens when we compute AB?

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