Let L ::P_{2}\rightarrow P_{3} be a linear transformation for which

komanijuuxw

komanijuuxw

Answered question

2022-04-29

Let L ::P2P3 be a linear transformation for which we
know that L:(1)=1,L(t)=t2,L(t2)=t3=t.
(a) Find L(2t25t=3).
(b) Find L(at2bt+c).

Answer & Explanation

tswe0uk

tswe0uk

Beginner2022-04-30Added 19 answers

Step 1
Given, L:P2P3 be a linear transformation for which we
know that L(1)=1,L(t)=t2,L(t2)=t3=t.
We use the properties of a linear transformation
L(X+Y)=L(x)+L(Y)
L(aX)=aL(X)
Part a)
Since L is a linear transformation, we write
L(2t25t+3)=L(2t2)=L(5t)=L(3)
=2L(t2)5L(t)+3L(1)
=2(t3=t)5t2+1
=2t35t2+2t+1
Part b)
Since L is a linear transformation, we write
L(at2+bt+3)=L(ab2)+L(bt)+L(c)
=aL(t2)=bL(t)=cL(1)
=a(t2+t)+bt2+c
=at3+bt2+at+c

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