Consider the Linear Transformation T:\mathbb{R}_2[x]\rightarrow \mathbb{R}_2[x] given by T(p(x))=p''(x) . Also A is the matrix of T with respect to the standard basis (1,x,x^2) .

Question

Consider the Linear Transformation   T:\mathbb{R}_2[x]\rightarrow \mathbb{R}_2[x]  given by   T(p(x))=p''(x) . Also   A  is the matrix of   T  with respect to the standard basis   (1,x,x^2)  .

Answer

A=\begin{pmatrix} 0 &0&2\0&0&0\0&0&0\end{pmatrix}

Answer

Eigen value is 0 and eigen vectors are spanned by   \{1,x\}  for   T

Answer

Eigen value is 0 and eigen vectors are spanned by   \{\begin{pmatrix} 1\0\0\end{pmatrix},\begin{pmatrix} 0\1\0\end{pmatrix}\}  for   A

Answer

Considering   T  means taking derivatives, it must be corrected as 
  T:\mathbb{R}_2[x]\rightarrow \mathbb{R}_0[x] . But then we don't have the linear transformation in the form   T:V\rightarrow V  and therefore eigen values/vectors are not defined.

Crowdly

Consider the Linear Transformation T:\mathbb{R}_2[x]\rightarrow \mathbb{R}_2[x...

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