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n. Justify your answers, 5. All polynomials of the form p(t) = at² , where a is in R. %3D 6. All polynomials of the form p(t) = a +t², where a is in R. 7. All polynomials of degree at most 3, with integers as coeffi- cients. 8. All polynomials in P, such that p(0) = 0. %3D 9. Let H be the set of all yectors of L17-

n. Justify your answers, 5. All polynomials of the form p(t) = at² , where a is in R. %3D 6. All polynomials of the form p(t) = a +t², where a is in R. 7. All polynomials of degree at most 3, with integers as coeffi- cients. 8. All polynomials in P, such that p(0) = 0. %3D 9. Let H be the set of all yectors of L17-

Advanced Engineering Mathematics
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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Number 6 and 8 please ?
15. vectors or a vector and a scalar-to show that H is not a subspace of R2. 4. Construct a geometric figure that illustrates why a line in R? not through the origin is not closed under vector addition. 17. In Exercises 5-8, determine if the given set is a subspace of P, for an appropriate value of n. Justify your answers, 19. If a mass m 1 pulled downwad begin to oscillate resting position i g 5. All polynomials of the form p(t) = at?, where a is in R. 6. All polynomials of the form p(t) = a +t², where a is in R. 7. All polynomials of degree at most 3, with integers as coefi- cients. y(t) = C cos ot + where o is a constas (See the figure bel described in (5) (w 8. All polynomials in P, such that p(0) = 0. -21 space. 9. Let H be the set of all vectors of the form Find a vector v in R³ such that H = Span {v}. Why does this show that H is a subspace of R3? 10. Let H be the set of all vectors of the form , where t is any real number. Show that H is a subspace of R3. (Use the method of Exercise 9.) 2b +3c 9- 2c 11. Let W be the set of all vectors of the form where b andc are arbitrary. Find vectors u and v such that W Span {u, v}. Why does this show that W is a subspace of R³? 20. The set of all cont closed interval [a, a subspace of the defined on [a, b]. 2s+4t a. What facts abc in order to derr 2s 12. Let W be the set of all vectors of the form 2s - 3t as claimed? calculus class.) Show that W is a subspace of R. (Use the method of Exercise 11.) b. Show that { in Cla, b). 13. Let v1 = = EA 2, and w = For fixed positive integ matrices is a vector spac of matrices and multiplia ,V2 2. a. Is w in {v1, V2, V3}? How many vectors are in {v1, V2, V3}? b. How many vectors are in Span {v1, V2, V3}? c. Is w in the subspace spanned by {V1, V2, V3}? Why? 21. Determine if the set is a subspace of M 14. Let v1, V2, V3 be as in Exercise 13, and let
Transcribed Image Text:15. vectors or a vector and a scalar-to show that H is not a subspace of R2. 4. Construct a geometric figure that illustrates why a line in R? not through the origin is not closed under vector addition. 17. In Exercises 5-8, determine if the given set is a subspace of P, for an appropriate value of n. Justify your answers, 19. If a mass m 1 pulled downwad begin to oscillate resting position i g 5. All polynomials of the form p(t) = at?, where a is in R. 6. All polynomials of the form p(t) = a +t², where a is in R. 7. All polynomials of degree at most 3, with integers as coefi- cients. y(t) = C cos ot + where o is a constas (See the figure bel described in (5) (w 8. All polynomials in P, such that p(0) = 0. -21 space. 9. Let H be the set of all vectors of the form Find a vector v in R³ such that H = Span {v}. Why does this show that H is a subspace of R3? 10. Let H be the set of all vectors of the form , where t is any real number. Show that H is a subspace of R3. (Use the method of Exercise 9.) 2b +3c 9- 2c 11. Let W be the set of all vectors of the form where b andc are arbitrary. Find vectors u and v such that W Span {u, v}. Why does this show that W is a subspace of R³? 20. The set of all cont closed interval [a, a subspace of the defined on [a, b]. 2s+4t a. What facts abc in order to derr 2s 12. Let W be the set of all vectors of the form 2s - 3t as claimed? calculus class.) Show that W is a subspace of R. (Use the method of Exercise 11.) b. Show that { in Cla, b). 13. Let v1 = = EA 2, and w = For fixed positive integ matrices is a vector spac of matrices and multiplia ,V2 2. a. Is w in {v1, V2, V3}? How many vectors are in {v1, V2, V3}? b. How many vectors are in Span {v1, V2, V3}? c. Is w in the subspace spanned by {V1, V2, V3}? Why? 21. Determine if the set is a subspace of M 14. Let v1, V2, V3 be as in Exercise 13, and let
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