- #1

foreverdream

- 41

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t: P

_{3}→ P

_{3}

p(x) → p(x) + p(2)

and s: P

_{3}→ P

_{2}

p(x) → p’(x)

thus

s o t gives P

_{3}→ P

_{2}gives

p(x) → p’(x)

next part says :

use the composite rule to find a matrix representation of the linear transformation s o t when

t: P

_{3 }→ P

_{3}

p(x) : p(x) + p(2)

and s: P

_{3 }→P

_{2}

p(x) → p’(x)

now my answer at the back says : it follows from the composite rule that the matrix of s o t with respect to standard bases for the domain and codomain is :

(matrix 1) composite (matrix 2 ) = (matrix 3)

¦0 1 0¦ composite ¦2 2 4 ¦ ¦ 0 1 0¦

¦0 0 2¦ composite ¦0 1 0 ¦= ¦0 0 2¦

¦0 0 1¦

Please explain how? apologies for using ¦ symbol instead of ( )for matrix as I don't know how to