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 to get .
Multiply by to get .
Multiply by to get .
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.
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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