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Chapter 2: Q56E (page 109)

TRUE OR FALSE?

If the linear system A2x鈫�=b鈫� is consistent, then the systemrole="math" localid="1659352762883" Ax鈫�=b鈫� must be consistent as well.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Inverse of a matrix

The inverse of matrix A=abcdis computed as,A-1=1ad-bcabcd

02

Consider the parameters.

Consider the consistent system.

A2x鈫�=b鈫�鈬�AAx鈫�=b鈫�鈭�Ax鈫�=A-1b鈫�

As the system A2x鈫�=b鈫�is consistent, thus, there exist an inverse of this system.

Therefore, Ax鈫�=b鈫�is consistent as well.

Hence, the given statement is true.

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