5. Left and Right Inverses: We have only talked about inverses of square matrices. This problem will explore the notion of a left and right inverse for a matrix that is not square. Let −1 (3) 0 A - a. Compute AAT, (AAT)−¹ and AT (AAT)-¹. You may use inv() function and matrix multplication in MATLAB or the Python equivalents (such as numpy.linalg.inv()). b. Show that the matrix B = AT (AAT)-¹ is a right inverse for A, i.e., verify that AB= I. Is BA = I? Let A be a m × n matrix with m > n, and suppose that the n x n matrix AT A C.
5. Left and Right Inverses: We have only talked about inverses of square matrices. This problem will explore the notion of a left and right inverse for a matrix that is not square. Let −1 (3) 0 A - a. Compute AAT, (AAT)−¹ and AT (AAT)-¹. You may use inv() function and matrix multplication in MATLAB or the Python equivalents (such as numpy.linalg.inv()). b. Show that the matrix B = AT (AAT)-¹ is a right inverse for A, i.e., verify that AB= I. Is BA = I? Let A be a m × n matrix with m > n, and suppose that the n x n matrix AT A C.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.3: M X N Matrices
Problem 49PS
Related questions
Question
![5.
Left and Right Inverses: We have only talked about inverses of square matrices.
This problem will explore the notion of a left and right inverse for a matrix that is not square. Let
To -1
A
1
0
=
1
a.
Compute AAT, (AAT)−¹ and AT (AAT)-¹. You may use inv() function and
matrix multplication in MATLAB or the Python equivalents (such as numpy.linalg.inv()).
b.
Show that the matrix B = AT (AAT)-¹ is a right inverse for A, i.e., verify that
AB= I. Is BA = I?
C.
Let A be a m × n matrix with m > n, and suppose that the n x n matrix AT A
is invertible. Suggest a formula of a left inverse C, i.e., find a matrix C such that CA = I. Your
expression for C should be in terms of A.
d.
Test formula of the left inverse from part (c) for the 2 x 1 matrix A
=
your
2
[3].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F039207b8-632a-4dc4-a3c4-fd77b3c684b4%2F3c24691f-e470-4cba-b68d-e674a72bc931%2F4rgvvr_processed.png&w=3840&q=75)
Transcribed Image Text:5.
Left and Right Inverses: We have only talked about inverses of square matrices.
This problem will explore the notion of a left and right inverse for a matrix that is not square. Let
To -1
A
1
0
=
1
a.
Compute AAT, (AAT)−¹ and AT (AAT)-¹. You may use inv() function and
matrix multplication in MATLAB or the Python equivalents (such as numpy.linalg.inv()).
b.
Show that the matrix B = AT (AAT)-¹ is a right inverse for A, i.e., verify that
AB= I. Is BA = I?
C.
Let A be a m × n matrix with m > n, and suppose that the n x n matrix AT A
is invertible. Suggest a formula of a left inverse C, i.e., find a matrix C such that CA = I. Your
expression for C should be in terms of A.
d.
Test formula of the left inverse from part (c) for the 2 x 1 matrix A
=
your
2
[3].
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