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Let $T : P_{2}(C) \to C^3$ be a linear transformation such that $$T(a + bx + cx^2) = (a, a + b, a + b + c)$$

Find the matrix representation $[T]$ relative to the standard bases.

I know how to do if it related to $R^n$ , but it is the same with C?

Let $T : P_{2}(C) \to C^3$ be a linear transformation such that $$T(a + bx + cx^2) = (a, a + b, a + b + c)$$

Find the matrix representation $[T]$ relative to the standard bases.

If standard basis for $R^3$,

$T(1,0,0)=(1,0,0)$

$T(0,1,0)=(1,1,0)$

$T(0,0,1)=(1,1,1)$

Therefore, $[T]$ = \begin{bmatrix}1&0&0\\1&1&0\\1&1&1\end{bmatrix}

But it is the same with $C^3$ ?

Let $T : P_{2}(C) \to C^3$ be a linear transformation such that $$T(a + bx + cx^2) = (a, a + b, a + b + c)$$

Find the matrix representation $[T]$ relative to the standard bases.

Let $T : P_{2}(C) \to C^3$ be a linear transformation such that $$T(a + bx + cx^2) = (a, a + b, a + b + c)$$

Find the matrix representation $[T]$ relative to the standard bases.

I know how to do if it related to $R^n$ , but it is the same with C?

Let $T : P2(C) → C^3$ be a linear transformation such that $T(a + bx + cx^2) = (a, a + b, a + b + c).$

Find the matrix representation [T] relative to the standard bases.

Let $T : P_{2}(C) \to C^3$ be a linear transformation such that $$T(a + bx + cx^2) = (a, a + b, a + b + c)$$

Find the matrix representation $[T]$ relative to the standard bases.