Linear Algebra Examples

Rewrite the vector set as a matrix.
Set up a system of equations based on the elements of each vector.
Simplify each term.
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Write the system of equations in matrix form.
Perform the row operation on (row ) in order to convert some elements in the row to .
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Replace (row ) with the row operation in order to convert some elements in the row to the desired value .
Replace (row ) with the actual values of the elements for the row operation .
Simplify (row ).
Use the result matrix to declare the final solutions to the system of equations.
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from both sides of the equation.
Subtract from both sides of the equation.
Subtract from both sides of the equation.
Since there are non-trivial solutions to the coefficient system, the set of polynomials is linearly dependent.
Linearly Dependent
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