Consider the vector space V of polynomials p(x) E P*(x) d? dr2 P(1) = 0 } . The dimension of V is four. satisfying Describe your isomorphism Iso by giving the elements of V satisfying the following: Iso(a1,0 + a1,1 x + aj,2 x² +a1,3 x³ + a\,4 xrt) = [1,0,0, 0] where Iso(a20 + a21 x + a22 x² +a23 x³ + az4 x* ) = [0, 1,0, 0] where Iso(a30 + a3,1 x + a3,2 x² + a3,3 x³ + a,a x* ) = [0, 0, 1, 0] where Iso(a4,0 + a4,1 x + a4,2 x² + a4,3 x³ + a44 x* ) = [0, 0, 0, 1] where Iso(as,0 + as,1 x + as,2 x² +as,3 x³ + as,4 x* ) = [-1,2, –3, –1] where
Consider the vector space V of polynomials p(x) E P*(x) d? dr2 P(1) = 0 } . The dimension of V is four. satisfying Describe your isomorphism Iso by giving the elements of V satisfying the following: Iso(a1,0 + a1,1 x + aj,2 x² +a1,3 x³ + a\,4 xrt) = [1,0,0, 0] where Iso(a20 + a21 x + a22 x² +a23 x³ + az4 x* ) = [0, 1,0, 0] where Iso(a30 + a3,1 x + a3,2 x² + a3,3 x³ + a,a x* ) = [0, 0, 1, 0] where Iso(a4,0 + a4,1 x + a4,2 x² + a4,3 x³ + a44 x* ) = [0, 0, 0, 1] where Iso(as,0 + as,1 x + as,2 x² +as,3 x³ + as,4 x* ) = [-1,2, –3, –1] where
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Evaluation: Determine Dimensions of Vector Spaces
Consider the vector space V of polynomials p(x) E P*(x) satisfying
d?
{
dv2 P(1) = 0 } . The dimension of V is four.
Describe your isomorphism Iso by giving the elements of V satisfying the following:
Iso(a1,0 + a1,1 x + a1,.2 x? + a1,3 x + a14 x*) = [1,0,0,0]
where
Iso(a2,0 + a2,1 x + a2.2 x² + a2,3 x³ + a24 x* ) = [0, 1,0, 0]
where
Iso(a3,0 + a3,1 x + a3,2 x? +a3,3 x + a34 ** ) = [0,0, 1, 0]
where
Iso(a4,0 + a4,1 x + a4,2 x² + a4,3 x³ + a4,4 x* ) = [0,0, 0, 1]
where
Iso(as,0 + as,1 x + as,2 x? +as,3 x + as4 x*) = [-1,2, -3, –1]
where](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12a8ea2c-67e8-49b8-8571-69dfee2b6790%2F77ae7dd1-753f-410b-ad4a-eeaba014b260%2Fovmbgl_processed.png&w=3840&q=75)
Transcribed Image Text:Evaluation: Determine Dimensions of Vector Spaces
Consider the vector space V of polynomials p(x) E P*(x) satisfying
d?
{
dv2 P(1) = 0 } . The dimension of V is four.
Describe your isomorphism Iso by giving the elements of V satisfying the following:
Iso(a1,0 + a1,1 x + a1,.2 x? + a1,3 x + a14 x*) = [1,0,0,0]
where
Iso(a2,0 + a2,1 x + a2.2 x² + a2,3 x³ + a24 x* ) = [0, 1,0, 0]
where
Iso(a3,0 + a3,1 x + a3,2 x? +a3,3 x + a34 ** ) = [0,0, 1, 0]
where
Iso(a4,0 + a4,1 x + a4,2 x² + a4,3 x³ + a4,4 x* ) = [0,0, 0, 1]
where
Iso(as,0 + as,1 x + as,2 x? +as,3 x + as4 x*) = [-1,2, -3, –1]
where
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