Question

33. Let $L: P_2(x) \rightarrow P_3(x)$ be a linear transformation defined by $L(f(x)) = x f(x) - (xf(x))'$, $\forall f(x) \in P_2(x)$. Find the represent matrix of the transformation $D$ under standard basis of $P_2(x)$ to standard basis of $P_3(x)$. Moreover, find the kernel and range of $L$.

Name: 33 let l p2x rightarrow p3x be a linear transformation defined by lfx x fx xfx forall fx in p2x find the represent matrix of the transformation d under standard basis of p2x to standard 20994
Uploaded: 2023-08-31T14:20:21-08:00
Duration: 2 min 25 s
Channel: Adi S
Description: 33 let l p2x rightarrow p3x be a linear transformation defined by lfx x fx xfx forall fx in p2x find the represent matrix of the transformation d under standard basis of p2x to standard 20994

          33. Let $L: P_2(x) \rightarrow P_3(x)$ be a linear transformation defined by
$L(f(x)) = x f(x) - (xf(x))'$, $\forall f(x) \in P_2(x)$.
Find the represent matrix of the transformation $D$ under standard basis of
$P_2(x)$ to standard basis of $P_3(x)$. Moreover, find the kernel and range of $L$.

33 let l p2x rightarrow p3x be a linear transformation defined by lfx x fx xfx forall fx in p2x find the represent matrix of the transformation d under standard basis of p2x to standard 20994

Added by Timothy S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/31/2023

Step 1

We need to find $L(1)$, $L(x)$, and $L(x^2)$. $L(1) = x(1) - (x(1))' = x - (x)' = x - 1 = -1 + x + 0x^2 + 0x^3$ $L(x) = x(x) - (x(x))' = x^2 - (x^2)' = x^2 - 2x = 0 + (-2)x + x^2 + 0x^3$ $L(x^2) = x(x^2) - (x(x^2))' = x^3 - (x^3)' = x^3 - 3x^2 = 0 + 0x + (-3)x^2 + Show more…

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33. Let $L: P_2(x) \rightarrow P_3(x)$ be a linear transformation defined by $L(f(x)) = x f(x) - (xf(x))'$, $\forall f(x) \in P_2(x)$. Find the represent matrix of the transformation $D$ under standard basis of $P_2(x)$ to standard basis of $P_3(x)$. Moreover, find the kernel and range of $L$.