Examples

Find the Null Space
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 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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