Linear Algebra Examples

Step 1
Write as an augmented matrix for .
Step 2
Find the reduced row echelon form.
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Step 2.1
Multiply each element of by to make the entry at a .
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Step 2.1.1
Multiply each element of by to make the entry at a .
Step 2.1.2
Simplify .
Step 2.2
Perform the row operation to make the entry at a .
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Step 2.2.1
Perform the row operation to make the entry at a .
Step 2.2.2
Simplify .
Step 2.3
Perform the row operation to make the entry at a .
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Step 2.3.1
Perform the row operation to make the entry at a .
Step 2.3.2
Simplify .
Step 2.4
Perform the row operation to make the entry at a .
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Step 2.4.1
Perform the row operation to make the entry at a .
Step 2.4.2
Simplify .
Step 2.5
Perform the row operation to make the entry at a .
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Step 2.5.1
Perform the row operation to make the entry at a .
Step 2.5.2
Simplify .
Step 2.6
Multiply each element of by to make the entry at a .
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Step 2.6.1
Multiply each element of by to make the entry at a .
Step 2.6.2
Simplify .
Step 2.7
Perform the row operation to make the entry at a .
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Step 2.7.1
Perform the row operation to make the entry at a .
Step 2.7.2
Simplify .
Step 2.8
Perform the row operation to make the entry at a .
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Step 2.8.1
Perform the row operation to make the entry at a .
Step 2.8.2
Simplify .
Step 2.9
Perform the row operation to make the entry at a .
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Step 2.9.1
Perform the row operation to make the entry at a .
Step 2.9.2
Simplify .
Step 2.10
Perform the row operation to make the entry at a .
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Step 2.10.1
Perform the row operation to make the entry at a .
Step 2.10.2
Simplify .
Step 3
Use the result matrix to declare the final solution to the system of equations.
Step 4
Write a solution vector by solving in terms of the free variables in each row.
Step 5
Write as a solution set.
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