# Matrices and Linear Systems of Equations

The augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate operations and describe the solution set of the original system.

1)

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2)

Solve the system.

3)

4)

Determine if the system is consistent. Don not completely solve but explain your answer.

5)

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

6)

Mark true or false and explain your answer.

a) every elementary row operation is reversible.
b) A 5×6 matrix has 6 rows.
c) The solution set of a linear system involving variables is a list of numbers ( ) that makes each equation in the system a true statement when the values are substituted for , respectively.
d) Two fundamental questions about a linear system involve existence and uniqueness.

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The augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate operations and describe the solution set of the original system.

1)

Solution. From the third row of this matrix , we can get a reduced equation which is
0=1
As 0=1 is impossible, we conclude that the original system has no solution.

2)

Solution. From the third row of this matrix , we can keep doing row operations to reduce it more. For instance, we use ½ to multiply the last row, so we have

Then we multiply the 4th row by 3 and add it onto the 3rd row, so we have

Then we multiply the 3rd row by 3 and add it onto the 2nd row, so we have

We add the 2nd row onto the first row to get

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