# Matrices : Row Operations and Echelon Form

1) An augmented matrix of a linear system has been reduced by row operations to the following form. Continue the appropriate row operations and describe the solution set of the original system.

Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave no details out. Thanks!

1 -2 0 3 -2

0 1 0 -4 7

0 0 1 0 6

0 0 0 1 -3

2) Solve the given augmented system.

Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave no details out. Thanks!

1 -3 4 -4

3 -7 7 -8

-4 6 -1 7

3) Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.

Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave no details out. Thanks!

a)h is just a variable right?

b)What does it mean a consistent linear system?

c) 1 h -3

-2 4 6

4) Row reduce the given matrix to educed echelon form. Circle the pivot positions in the final matrix and in the original matrix, and list the pivot columns.

Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave no details out. Thanks!

1 3 5 7

3 5 7 9

5 7 9 1

https://brainmass.com/math/linear-algebra/matrices-row-operations-echelon-form-32213

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1) An augmented matrix of a linear system has been reduced by row operations to the following form. Continue the appropriate row operations and describe the solution set of the original system.

1 -2 0 3 -2

0 1 0 -4 7

0 0 1 0 6

0 0 0 1 -3

Solution. We use r2+4*r4 to denote an operation: the 4th row times 4, then add on the second row. We get

1 -2 0 3 -2

0 1 0 0 -5

0 0 1 0 6

0 0 0 1 -3 ...

#### Solution Summary

Matrix Row Operations and Echelon Form are investigated. The solution is detailed and well presented.