POWER SYSTEM ANALYSIS+DESIGN-EBK >I<
POWER SYSTEM ANALYSIS+DESIGN-EBK >I<
6th Edition
ISBN: 9781337259170
Author: Glover
Publisher: INTER CENG
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Chapter 6, Problem 6.1MCQ

For a set of linear algebraic equations in matrix format, A x y , for a unique solution to exist, det(A) should be __________.

Expert Solution & Answer
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To determine

To fill in the blank space: For a set of linear algebraic equations in matrix format, Ax=y , for a unique solution to exist, det(A) should be ________.

Answer to Problem 6.1MCQ

For a set of linear algebraic equations in matrix format, Ax=y , for a unique solution to exist, det(A) should be non-zero.

Explanation of Solution

Given:

A set of linear algebraic equations in matrix format, Ax=y .

If det(A)0 , it follows that A1=adj(A)det(A) is defined and exists.

Multiplying A1 to the left of both sides of the matrix equation Ax=y , we get,

A1Ax=A1yIx=A1yx=A1y

This implies that the solution of the given matrix equation is x=A1y .

For a given matrix A , A1 is uniquely defined.

Then, for given matrices A and y , x=A1y is unique.

Thus, if det(A)0 , Ax=y has a unique solution.

So, filling in the blank space in the given statement:

For a set of linear algebraic equations in matrix format, Ax=y , for a unique solution to exist, det(A) should be non-zero.

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