Question: Consider the linear transformation \(T:{{P}_{2}}\to {{P}_{2}}\) defined as: \(T\left( p\left( x \right) \right)=p\left( 3x+2 \right)\) for each \(p\left( x \right)\in {{P}_{2}}\)

1. Use the definition above to find \(T\left( 3-2x+5{{x}^{2}} \right)\)
2. Find the matrix A that represents T, and use the matrix A to find \(T\left( 3-2x+5{{x}^{2}} \right)\)
3. Find \(\ker \left( T \right)\), a basis for \(\ker \left( T \right)\), and \(\dim\ker \left( T \right)\). Is T a 1-1? Explain.
4. Find R(T), a basis for R(T), and dim( R(T)). Is T onto? Explain.

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document