In Exercises 1 − 10 , the linear transformations S , T , H are defined as follows: S : P 3 → P 4 is defined by S ( p ) = p ′ ( 0 ) . T : P 3 → P 4 is defined by T ( p ) = ( x + 2 ) p ( x ) . H : P 4 → P 3 is defined by H ( p ) = p ′ ( x ) + p ( 0 ) . Also, B = { 1 , x , x 2 , x 3 } is the natural basis for P 3 and C = { 1 , x , x 2 , x 3 , x 4 } is the natural basis for P 4 . Find the matrix for S with respect to B and C .
In Exercises 1 − 10 , the linear transformations S , T , H are defined as follows: S : P 3 → P 4 is defined by S ( p ) = p ′ ( 0 ) . T : P 3 → P 4 is defined by T ( p ) = ( x + 2 ) p ( x ) . H : P 4 → P 3 is defined by H ( p ) = p ′ ( x ) + p ( 0 ) . Also, B = { 1 , x , x 2 , x 3 } is the natural basis for P 3 and C = { 1 , x , x 2 , x 3 , x 4 } is the natural basis for P 4 . Find the matrix for S with respect to B and C .
Solution Summary: The author explains the matrix for S with respect to B and C.
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