onsider the multiplication operator LA: R² R² defined by LA(z) = Az where A = -6 is the standard basis. 1= .b₂ == Find an ordered basis B= (b₁,b₂) for R² such that [L] = 37 15 -96-39 Hint: [LA] = A where

Q: Determine whether S is a basis fa S = {9 – t, t³, 6t², 2t +

A: S is the basis of P3 if the vectors are linearly independent. Therefore for the vectors to be…

Q: 3. Let X = {(1) (1) (1) ()}. a) Show that X spans R³. b) Explain why X is not a basis for R³. c)…

A:

Q: Explain why S is not a basis for R². s={(6, 8), (1, 0), (0, 1)) S is linearly dependent. OS does not…

A: We will use S to determine which among the given options is correct.

Q: vi = (x, 1,1) , v2 = (1, x, 1) v3 = (1,1, x) %3D %3D %3D S = { v1, v2, V3} For the set S to be a…

A:

Q: An orthogonal basis for A, - 10 -8 6 2 4 -6 -8 16 16 30 23 4 4 1 2 1 4 11 6-3, is with the given…

A:

Q: Constants: a = 2, b = 3 c. Find global position x when [x]B = 1 2 . d. Using your answer for x from…

A:

Q: 6C Illustration is given f: R³ R³: (x, y, z)→f(x, y, z) = (x-2y, y-2z, -x+4=) Find the basis change…

A:

Q: Explain why, no matter how the circuit is completed, Pip must place an even number of additional…

A:

Q: A BASIS FOR Q-DESCRIBE THE BASIS IN ROSTER THE ELEMENT IN INCREASING GIVEN ENENSION OVE METHOD. LIST…

A:

Q: The set B = {3 - 3x², 6 + 2x − 6x², 7 + 4x − 6x²} is a basis for P2. Find the coordinates of p(x) =…

A:

Q: The conjugate z of z=x+iy is z=x-iy

A: 4) Conjugate of a complex number: The complex conjugate is obtained by changing the sign of the…

Q: 2,0 10 10 Find the coordinates of æ in the ordered basis B = (a, b). Hint: The preview shows the…

A: From the graph can write, x=-6,4a=-2,6b=-4,-4

Q: A 2-4 284-6 0 23 05 0 -5 6. 5. 2. 12 4-1 6. -9 15 L3 4 -58 a) find basis for col(A) Find basis for…

A:

Q: The set B={1-1²,1-1², 1+2t-12) is a basis for P₂. Find the coordinate vector of p(t) = -1+6t-3t²…

A:

Q: Let T : R3 R3 be a linear map and S be the standard basis.Ouestion m De 2 0 2 25 4 37 1 :00 AT S-S…

A:

Q: A = [aj a2 az] -1 -2 -3 %3D 0 1 -2 (iii.) Find the orthogonal projection of Jonto the column space…

A: we have, A=14-1-1-2-301-2 Apply R2→R1+R2 =14-102-401-2R3→R3-12R2 14-102-4000 we have two pivot…

Q: Consider the multiplication operator LA: R² R² defined by LA(x) = Ax where A = 6 [LAB= Hint: [LA] A…

A:

Q: The vectors u, v, w have the coordinates (-6, 2, 1), (2. -1,0) and (7. -2, -1) respectively relative…

A:

Q: Let L be the line spanned by TOOT -1 0 -8 -7 in R4. Find a basis of the orthogonal complement L¹ of…

A:

Q: Let S be the standard basis for IR and consider the non-standard ordered bases of R4 1 3 -1 3 1 -2…

A:

Q: Suppose that you have $11,000 in a rather risky investment recommended by your financial advisor.…

A:

Q: Results for this submission J At least one of the answers above is NOT correct. T(6₂) = 86₁ +26₂. )…

A:

Q: 1 Let A = 1 d where c, d denote real numbers. 0 0 0 3 If a basis for im(A) is and a basis for…

A:

Q: B1 Be ß1 and B2, bases of R´, and denote by [1] the base B2 change matrix B1 to the base B2 . Given…

A: Given that the change of the basis matrix is Iβ1β2=5-2-21 Also the coordinates of the vector with…

Q: = {(: ") e v : a,b,c, € F}, w. = { (; ") : a, 6.c € F}- a b { (; 2) : a,6, c € F}. Find the basis…

A:

Q: 8- 3 3 (a) Find the coordinate vector of a = of R³. (b) Let F₁ be the ordered basis of R2 given by…

A:

Q: Find a basis for N(A) and give the nullity and the rank of A. -1 2 0 A 2 -5 1

A: Suppose A is any mxn matrix then RankA+NullityA=n

Q: The following matrix is the transition matrix from S to some other basis of R³. 2 -1 3 -1 -1 0 1 2…

A: Basis of linear transmission

Q: Which of the following is not a basis for R3. A. {(1,1, 1), (1, 1,0), (1,0, 0)} B. {(1,0,0), (0,…

A:

Q: In a rectangle, the width is one-third the length. The total perimeter is 40 inches. Find the length…

A: Solution: Given:    Width is one third of the length of rectangle     and the perimeter of rectangle…

Q: Quest In P₂, let B and C be the bases where B = {1-312, 2+t-5t2, 1+2t) and the standard basis C =…

A: I have given the answer in the next step. Hope you understand that

Q: 5. Find the function ax6 + bx5 + c which is closest to x on the interval [−1, 1]. Find an orthogonal…

A:

Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x2} || O sis linearly dependent.…

A: