Find the set of all polynomial in such that , and determine its dimension.
The dimension of such that is which is spanned by .
Consider the set of all polynomial such that .
The set is linear independent set V of if there exist constant such that where .
Any polynomial is defined as follows.
Substitute the value 1 for t in the equation as follows.
As , substitute the value 0 for in the equation as follows.
Substitute the value for in the equation as follows.
From the equation, the set span if .
Compare the equations both side as follows.
By the definition of linear independence, the subset is L.I.
Therefore, the set of all polynomial such that has dimension 2 and spanned by .
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