- #1
tas3113
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I have two questions that I don't really understand what it's asking for. Can someone help me get started please?
1. Find a linear map from P4 to P4 (where P4 is the space of polynomials of degree less than 4) whose kernel is one-dimensional. Find one whose kernel is two-dimensional.
what im thinking is:
if it is a map in P4, then it looks like
[tex]
\left|\begin{array}{ccc}1 \\ x\\ x^2\\x^3\end{array}\right|
[/tex]
?? not sure where to go from there.
2. Find the matrix representation in the standard basis of the linear transformation from P4 to P3:
f(x) -> 2f(x) - f(x-1) - f(x+1).
What is the dimension of its kernel? Of its image?
absolutely no idea where to begin
1. Find a linear map from P4 to P4 (where P4 is the space of polynomials of degree less than 4) whose kernel is one-dimensional. Find one whose kernel is two-dimensional.
what im thinking is:
if it is a map in P4, then it looks like
[tex]
\left|\begin{array}{ccc}1 \\ x\\ x^2\\x^3\end{array}\right|
[/tex]
?? not sure where to go from there.
2. Find the matrix representation in the standard basis of the linear transformation from P4 to P3:
f(x) -> 2f(x) - f(x-1) - f(x+1).
What is the dimension of its kernel? Of its image?
absolutely no idea where to begin