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Let H={p() : p()= a + b + cf*: a,b,cer} (a)(3 marks) Show that H is...
== Let P3 have the inner product given by evaluation at -3, -1, 1, and 3....
== Let P3 have the inner product given by evaluation at -3, -1, 1, and 3. Let po(t) = 4, p1(t)=t, and t² – 5 q(t) = Notice that these polynomials form an orthogonal set with this inner product. Find the best 4 approximation to p(t) = tº by polynomials in Span{P0,21,9}. The best approximation to p(t) = tº by polynomials in Span{Po.21,93 is
4 2-5 Notice that these polynomials form an Let P3 have the inner product given by...
4 2-5 Notice that these polynomials form an Let P3 have the inner product given by evaluation at -3, -1, 1, and 3. Let po(t) = 2, P (t) = 4t, and act) = orthogonal set with this inner product. Find the best approximation to p(t) = tº by polynomials in Span{Po-P1:9). The best approximation to p(t) = tº by polynomials in Span{Po.P7.93 is
Let Ps have the inner product given by evaluation at -2, -1, 1, and 2. Let po(t)-1. P,()-t, and p...
Let Ps have the inner product given by evaluation at -2, -1, 1, and 2. Let po(t)-1. P,()-t, and p20)- a. Compute the orthogonal projection of p2 onto the subspace spanned by Po and P1 b. Find a polynomial q that is orthogonal to Po and p,, such that Po P is an orthogonal basis for Span(Po P1, P2). Scale the polynomial q so that its vector of values at a2(Simplify your answer.)
Let Ps have the inner product given...
Answer Question #12. Question #11 is only for reference 11. Let po, pi, and p2 be...
Answer Question #12. Question #11 is only for reference
11. Let po, pi, and p2 be the orthogonal polynomials described in Example 5, where the inner product on P4 is given by evaluation at -2, -1, 0, 1, and 2. Find the orthogonal projection of tonto Span {po, pi, p2). 12. Find a polynomial p3 such that {po, p1, p2.p3} (see Exercise 11) is an orthogonal basis for the subspace P3 of P4. Scale the polynomial p3 so that its...
Let H be the set of third degree polynomials H = {ax + ax2 + ax...
Let H be the set of third degree polynomials H = {ax + ax2 + ax aEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). 0 a. H is a subspace of P3 because it contains only second degree polynomials 1b. H is a subspace of P3 because it can be written as the span of a subset of P3 OcH is not a subspace of P3...
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem...
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem 1, Section 4.3 and Problem 1, Section 4.6 that W is a subspace of P3. Let T:W+Pbe given by T(p(t)) = p' (t). It is easy to check that T is a linear transformation. (a) Find a basis for and the dimension of Range T. (b) Find Ker T, a basis for Ker T and dim KerT. (c) Is T one-to-one? Explain. (d) Is...
Let p, (t) 6+t, P2(t) =t-3t, p3 (t) = 1 +t-2t. Complete parts (a) and (b) below. Use coordinate vectors to show that th...
Let p, (t) 6+t, P2(t) =t-3t, p3 (t) = 1 +t-2t. Complete parts (a) and (b) below. Use coordinate vectors to show that these polynomials form a basis for P2. What are the coordinate vectors corresponding to p, p2, and pa? P- Place these coordinate vectors into the columns fa matrix A. What can be said about the matrix A? O A. The matrix A forms a basis for R3 by the Invertible Matrix Theorem because all square matrices are...
Notice that these polynomials form an orthogonal set with this inner product. Find the best 1²-13...
Notice that these polynomials form an orthogonal set with this inner product. Find the best 1²-13 Let P2 have the inner product given by evaluation at -5, -1, 1, and 5. Let po(t) = 2, P1(t)=t, and q(t) = 12 approximation to p(t) = t by polynomials in Span{Po.P1,9}. The best approximation to p(t) = t by polynomials in Span{Po.P2,q} is
6.Let W={(a +b-c,2a +3b, -a +3c,-b-2c): a,b, CER) a) For what value of n is W...
6.Let W={(a +b-c,2a +3b, -a +3c,-b-2c): a,b, CER) a) For what value of n is W isomorphic to R"?, clear answer the question and justify your answer b) Find an isomorphism T:R" W for the value of n you found in part (a).Please make it clear from your work that your function T is really an isomorphism. 7.Let T:P2(R) – P2(R) be a linear transformation such that T(x2)=x2 a) Prove that if there exist distinct linearly independent polynomials 2,9 €...
linear algebra 2 part mcq part a part b H Let be the set of third...
linear algebra 2 part mcq
part a
part b
H Let be the set of third degree polynomials H = {ax + ax? + ax' | AEC) P3 why or why not? H Is a subspace of Select all correct answer choices (there may be more than one). a. H P3 is a subspace of because it can be written as the span of a subset of b. H is a subspace of because it contains only second degree polynomials...
== Let P3 have the inner product given by evaluation at -3, -1, 1, and 3. Let po(t) = 4, p1(t)=t, and t² – 5 q(t) = Notice that these polynomials form an orthogonal set with this inner product. Find the best 4 approximation to p(t) = tº by polynomials in Span{P0,21,9}. The best approximation to p(t) = tº by polynomials in Span{Po.21,93 is
4 2-5 Notice that these polynomials form an Let P3 have the inner product given by evaluation at -3, -1, 1, and 3. Let po(t) = 2, P (t) = 4t, and act) = orthogonal set with this inner product. Find the best approximation to p(t) = tº by polynomials in Span{Po-P1:9). The best approximation to p(t) = tº by polynomials in Span{Po.P7.93 is
Let Ps have the inner product given by evaluation at -2, -1, 1, and 2. Let po(t)-1. P,()-t, and p20)- a. Compute the orthogonal projection of p2 onto the subspace spanned by Po and P1 b. Find a polynomial q that is orthogonal to Po and p,, such that Po P is an orthogonal basis for Span(Po P1, P2). Scale the polynomial q so that its vector of values at a2(Simplify your answer.)
Let Ps have the inner product given...
Answer Question #12. Question #11 is only for reference
11. Let po, pi, and p2 be the orthogonal polynomials described in Example 5, where the inner product on P4 is given by evaluation at -2, -1, 0, 1, and 2. Find the orthogonal projection of tonto Span {po, pi, p2). 12. Find a polynomial p3 such that {po, p1, p2.p3} (see Exercise 11) is an orthogonal basis for the subspace P3 of P4. Scale the polynomial p3 so that its...
Let H be the set of third degree polynomials H = {ax + ax2 + ax aEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). 0 a. H is a subspace of P3 because it contains only second degree polynomials 1b. H is a subspace of P3 because it can be written as the span of a subset of P3 OcH is not a subspace of P3...
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem 1, Section 4.3 and Problem 1, Section 4.6 that W is a subspace of P3. Let T:W+Pbe given by T(p(t)) = p' (t). It is easy to check that T is a linear transformation. (a) Find a basis for and the dimension of Range T. (b) Find Ker T, a basis for Ker T and dim KerT. (c) Is T one-to-one? Explain. (d) Is...
Let p, (t) 6+t, P2(t) =t-3t, p3 (t) = 1 +t-2t. Complete parts (a) and (b) below. Use coordinate vectors to show that these polynomials form a basis for P2. What are the coordinate vectors corresponding to p, p2, and pa? P- Place these coordinate vectors into the columns fa matrix A. What can be said about the matrix A? O A. The matrix A forms a basis for R3 by the Invertible Matrix Theorem because all square matrices are...
Notice that these polynomials form an orthogonal set with this inner product. Find the best 1²-13 Let P2 have the inner product given by evaluation at -5, -1, 1, and 5. Let po(t) = 2, P1(t)=t, and q(t) = 12 approximation to p(t) = t by polynomials in Span{Po.P1,9}. The best approximation to p(t) = t by polynomials in Span{Po.P2,q} is
6.Let W={(a +b-c,2a +3b, -a +3c,-b-2c): a,b, CER) a) For what value of n is W isomorphic to R"?, clear answer the question and justify your answer b) Find an isomorphism T:R" W for the value of n you found in part (a).Please make it clear from your work that your function T is really an isomorphism. 7.Let T:P2(R) – P2(R) be a linear transformation such that T(x2)=x2 a) Prove that if there exist distinct linearly independent polynomials 2,9 €...
linear algebra 2 part mcq
part a
part b
H Let be the set of third degree polynomials H = {ax + ax? + ax' | AEC) P3 why or why not? H Is a subspace of Select all correct answer choices (there may be more than one). a. H P3 is a subspace of because it can be written as the span of a subset of b. H is a subspace of because it contains only second degree polynomials...
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