Proving(AT)−1=(A−1)T:

For any matrix A,

A-1A=I

Now, by post taking transpose on both the sides, the following expression is obtained,

(A-1A)T=IT =I

This can be written as follows,

(A-1)TAT=I

Now, by post multiplying the expression with (AT)<

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Introduction to mathematical programming

Ch. 2.1 - Prob. 1P Ch. 2.1 - Prob. 2P Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - Prob. 7P Ch. 2.2 - Prob. 1P Ch. 2.3 - Prob. 1P Ch. 2.3 - Prob. 2P

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Proving ( A T ) − 1 = ( A − 1 ) T : For any matrix A, A - 1 A = I Now, by post taking transpose on both the sides, the following expression is obtained, ( A - 1 A ) T = I T = I This can be written as follows, ( A - 1 ) T A T = I Now, by post multiplying the expression with ( A T )<

Solution Summary: The author explains that by post taking transpose on both the sides, the following expression is obtained, Beginarrayl(A-1)T

Concept explainers

Explanation of Solution

Proving(AT)−1=(A−1)T:

For any matrix A,

A-1A=I

Now, by post taking transpose on both the sides, the following expression is obtained,

(A-1A)T=IT =I

This can be written as follows,

(A-1)TAT=I

Now, by post multiplying the expression with (AT)<

Want to see the full answer?

Chapter 2 Solutions

Proving ( A T ) − 1 = ( A − 1 ) T : For any matrix A, A - 1 A = I Now, by post taking transpose on both the sides, the following expression is obtained, ( A - 1 A ) T = I T = I This can be written as follows, ( A - 1 ) T A T = I Now, by post multiplying the expression with ( A T )&lt;

Solution Summary: The author explains that by post taking transpose on both the sides, the following expression is obtained, Beginarrayl(A-1)T

Concept explainers

Explanation of Solution

Proving(AT)−1=(A−1)T: For any matrix A, A-1A=I Now, by post taking transpose on both the sides, the following expression is obtained, (A-1A)T=IT =I This can be written as follows, (A-1)TAT=I Now, by post multiplying the expression with (AT)<

Want to see the full answer?

Chapter 2 Solutions

Proving ( A T ) − 1 = ( A − 1 ) T : For any matrix A, A - 1 A = I Now, by post taking transpose on both the sides, the following expression is obtained, ( A - 1 A ) T = I T = I This can be written as follows, ( A - 1 ) T A T = I Now, by post multiplying the expression with ( A T )<

Proving(AT)−1=(A−1)T:

For any matrix A,

A-1A=I

Now, by post taking transpose on both the sides, the following expression is obtained,

(A-1A)T=IT =I

This can be written as follows,

(A-1)TAT=I

Now, by post multiplying the expression with (AT)<