The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assumethe vectors are in the order X₁, X₂-*A-7CO- 6The orthogonal basis produced using the Gram-Schmidt method for Wis.(Type a vector or list of vectors. Use a comma to separate vectors as needed.)

The given basis for subspace using Gram-Schmidit process will produce an orthogonal basis for .

Answered: The set is a basis for a subspace W.…

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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Let B be the standard basis of the space P, of polynomials.Use coordinate vectors to test whether the following set of polynomials span P,. Justify your conclusion. 1-2t + 3, -4+6t – 81, -2+3t - 4?, 2- 3t + 412 Does the set of polynomials span P,? O A. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R°. By isomorphism between R and P, , the set of polynomials does not span P,. O B. Yes; since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position in each row, the set of coordinate vectors spans R3. By isomorphism between R3 and P, , the set of polynomials spans P2- O C. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R2. By isomorphism between R2 and P,, the set of polynomials does not span P,. O D. Yes;…
: Let p 8x2 + 4x + 3. Find the coordinate vector of p relative to the following basis for P2, 1, p2 = 1+x, P3 = 1+x+x².
Oa + Ob + 0c +4d la + (-1) b+ (-2) c +4d 0a+1b+ (-2) c +5d la + (-1) b + (-2) c + 2d 2a + 1b+ (-10) c +4d Then an orthogonal basis for Range(T) would be: Note that if you do not need a basis vector, then write 0 for all entries of that basis vector. For example, if you only need 2 vectors in your basis, then write 0 in all boxes corresponding to the third vector 1) Let T a [25] =
please dont provide hand written solution K If B is the standard basis of the space P3 of polynomials, then let B = {1, t, t², t³). Use coordinate vectors to test the linear independence of the set of polynomials below. Explain your work. (-3-t)³, (-2-t)², 31+31t+10² +³ Write the coordinate vector for the polynomial (-3-t)³, denoted p₁.
Find the B-coordinate vector of x E H where B = {b₁,b₂} is a basis of subspace H. b₁ = H b₂ = [1] 3 - x = 2 图 2
Consider two bases B = {b1,b2} andC : such that bị = cq – 4c2 and b2 = 6c1 – 5c2. Find the change-of- coordinates matrix from B to C. {C1, c2} for a vector space V, %3D %3D 6. 4 -5 1 6 4 5 1-4 6. -5 1 -4 -5
2. Find the coordinate vector [x] of a relative to the given basis B = {b₁,b2, b3} . b₁ = -1 , b₂ = -3 4 9 b3 = 2 -2 4 ,x= 8 -9 6
Let B be the standard basis of the space P₂ of polynomials. Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. - 5t+t², 1+5t-t²2, 2+t+t², +8t-3t² G Does the set of polynomials span P₂? O A. Yes; since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position in each row, the set of coordinate vectors spans R². By isomorphism between R² and P2, the set of polynomials spans P2. O B. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R³. By isomorphism between R³ and P2, the set of polynomials does not span P2. OC. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R². By isomorphism between R² and P2, the set of polynomials does not span P2. ⒸD. Yes; since the…
a
Let X = TONT. 1 and 3 0 A = 0 3 1 0 -2 -4 -4 0 3 00 -2 00 -4 0 1 -1 01 1 0 0
R is the reduced row echelon form of Q. Find a basis {b₁,b2, ..., bn} for the null space of Q. b₁ = b₂ Fill in vectors in numerical order. Leave blank those that are not needed. = b3 b4 = b5 = 6565 7070 -704 -306 4480 -1573 1694 168 74 - 1073 1579 2314 2492 -248 -108 8138 8764 872 -380 5553 -2613 3317 - 794 1169; R = 4111 -2814 280 122 -1783 - 1320 = 1 0 13 00 1 00 0 0 0 0 0 0 0 2 13 1 0 0 0 8 13 8 0 0 0 10 | 5 13 8 0 0
Find the representation of (-5, 5, 1) in each of the following ordered bases. Your answers should be vectors of the general form . a. Represent the vector (-5, 5, 1) in terms of the ordered basis B = {ï,j,k}. [(-5, 5, 1)]B= b. Represent the vector (-5,5, 1) in terms of the ordered basis C = (ē3, ē1, ë2). [(-5, 5, 1)]c = c. Represent the vector (-5, 5, 1) in terms of the ordered basis D = {-2, -ē1, ē3}. [(-5, 5, 1)]D=

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