Answered: For Exercise, an augmented matrix is…

For Exercise, an augmented matrix is given. Determine the number of solutions to the corresponding system of equations. 0 |-3 4 1

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.2: Guassian Elimination And Matrix Methods

Problem 89E

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Question

For Exercise, an augmented matrix is given. Determine the number of solutions to the corresponding system of equations.
0 |-3
4
1

Expert Solution

Step 1

The nature and number of solutions of a given system of equations can be predicted by augmented matrix method which deals with finding out the ranks of augmented matrix and coefficient matrix.

To find the rank, the augmented matrix is first converted to its row echelon form. From the row echelon form, the number of rows which consist of at least one non zero element is the rank of the matrix.