Suggested languages for you:

Americas

Europe

Q4Q

Expert-verifiedFound in: Page 1

Book edition
5th

Author(s)
David C. Lay, Steven R. Lay and Judi J. McDonald

Pages
483 pages

ISBN
978-03219822384

**Suppose the coefficient matrix of a linear system of three equations in three variables has a pivot position in each column. Explain why the system has a unique solution.**

The system has a unique solution because it is row reduced to an identity matrix of the order \(3 \times 3\).

The system of three equations is fulfilled if the three planes cross at a single location. ** **

As a result, the echelon form that can be produced by solving this system of equations is an identity matrix of the order \(3 \times 3\).

Thus, the echelon form of the consistent linear system is an identity matrix of the order \(3 \times 3\).

It is given that the coefficient matrix of a linear system of three equations in three variables has a pivot position in each column. So, the system in span \({\mathbb{R}^3}\) is row reduced to identity matrix echelon form.

Thus, the system has a unique solution.

94% of StudySmarter users get better grades.

Sign up for free