9. Let vi = (1, 1, 3, 2, -1) and v2 = (2, 2, 1, -2, 0). Let W = span{v1, v2}. %3D (a) Find the orthogonal complement of W (that is, w+). Write a basis for W+. (b) Give the dimension of W, and the dimension of W+.

Q: 4. Let {V1,... , Vn} be an orthogonal basis of R". For any vectors x, y in R" show that (x · V;) (y…

A:

Q: The Gram-Schmidt process transforms the basis u=(-1, 3), u2=(7, – 1) of R²into the orthogonal basis…

A: We have given the basis u1=-1,3 and u2=7,-1. The Gram-Schmidt process to convert basis into the…

Q: 2. Let L1 bg 3D (-1,2, 1,3, 3), сі %3D (3, —4, 0, — 4, 3), сэ %3D Find a basis of Lin L2 and L1+ L2.…

A:

Q: Given the vectors X1 2 X2 = 3 X3 = X4 = 2 5 3 (a) Are x1, X2, X3, and x4 linearly independent in R'?…

A: Basis : A collection of vectors of R³ is said to be basis of a R³ if  They are linearly…

Q: 18. Use the Gram-Schmidt process to transform the given basis (w, w, orthogonal basis where w =…

A:

Q: Let B = (1, x, x², x*) be an ordered basis for P3. Find the coordinate vector of 8x – 6x2 – 9x + 3…

A:

Q: Find a basis of R that contains the vectors X = (1,1,1,1) and Y = (1,1,0,1).

A: Given Vectors X =(1,1,1,1) and Y = (1,1,0,1) Now determine the orthogonal basis for R4

Q: 4. (a) Let L be the line in R' spanned by the vector (1,1, 1, 1). Find a basis for the orthogonal…

A:

Q: Answer the following questions about the Gram-Schmidt process for obtain- ing an orthogonal basis…

A:

Q: Recall that B = {1+2x,3 – x}. Let the vector space P¡ have the inner product (p, q) = 2aobo + 3a¡b¡…

A: Given B=1+2x,3-x is basis of the vector space P1. The inner product , defined on P1 as follows:…

Q: §8.3, Exercise 1. Let wi = (1,4) and w2 = (-2, 1). %3D Find the coordinates of v = (-1,32) in the W…

A:

Q: 1) Interpolate (by hand) the data x = [-1,0,1] %3D y = [0,1,3] using a) the linear spline basis;

A:

Q: Find the matrix for T relative to the basis B, and use Theorem 8.5.2 to compute the matrix for T…

A:

Q: The Gram-Schmidt process transforms the basis u,=(1, 3), u,=(1, –7) of R² into the orthogonal basis…

A:

Q: -3' 2, uz [3] -4 is an orthogonal basis of R3 and x = 2 Let u1 1, u3 4 If x can be expressed as a…

A:

Q: 1. Find the coordinates of vector w (1,2, 3) in the basis A which consists of T1 = (1, 1, 0), 72 =…

A:

Q: The Gram-Schmidt process transforms the basis u= (1, -2) , u2= (2, 6) of R into the orthogonal basis…

A:

Q: Let S = {vi, v2, v3} where v = (1,0,1), = (1,1,0) and (0,0,1) be a basis of R³. Let T = %3D %3D %3D…

A: Given: PS,T=12-111-1221S=1,0,1,1,1,0,0,0,1

Q: Find the matrix A' for T relative to the basis B'. T: R > R, Tх, у, z) %3D (у — z, х - z, х + у), В'…

A:

Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector of f(x) = - 823 6x? –…

A: ANSWER :

Q: The Gram-Schimidt process transforms the basis u=(1, 3), u2-(1, -7) of R intothe orthogonal basis…

A: Given u1=⟨1,3⟩,u2=⟨1,−7⟩

Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) - (-5x + y, 5x - y), B'- ((1,…

A:

Q: 6. Let B= {(v,,V½, v½ } be a basis for R'. Use the Gram-Schmidt process to find an orthogonal basis.…

A: We need to find the orthogonal basis of R3 . The basis here is {v1 , v2 ,v3 } and we do not need to…

Q: 15. Use the Gram-Schmidt process to transform the basis {r1, x2, a3, T4} into an orthogonal basis…

A:

Q: Let S = {u1, uz2, U3, U4} C Rª, where (1,1, 1, 1), U2 = (1, 1, – 1, –1), (1,—1,1, —1), и4 — (1, –1,…

A: As per the guidelines I solved your first three subparts of the question. For more solutions please…

Q: Determine whether the set S {1 – t, t, 1 + t²} a. Spans P2 b. Is linearly independent c. Is a basis…

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: Let A = -1 -9 3

A:

Q: Find the orthogonal complement W⊥ of W and give a basis for W ⊥

A:

Q: Let V = R2, W = span({(1, 2)}), and β be the standard ordered basis for V. Compute [T]β, where T is…

A: Let

Q: 4. Let {V1, ... , Vn} be an orthogonal basis of R". For any vectors x, y in R" show that Σ (х - V,)…

A:

Q: then the second coordinate of the vector in the basis is: (3,5,7) If B=((1,1,1),(1,0, 1), (0,1, 1))…

A:

Q: 15. Use the Gram-Schmidt process to transform the basis {x1, 2, 23, x4} into an orthogonal basis for…

A:

Q: The Gram-Schmidt process transforms the basis u3(1,-3), u,=(-7, 1) of R into the orthogonal basis…

A:

Q: 8. Let W = Span{v1, v2}. Find an orthonormal basis for W. Vị = -2 , V1 = 4 2

A: An orthonormal basis for an inner product space V with finite dimension is a basis for V whose…

Q: Let B = uj = ,U2 = and C = , V2 = Find Pc, the transition matrix %3D from the standard basis of R2…

A:

Q: Let B = {v1, v2, V3} be a basis for R3. For any u, v E R³ define || (u, v) = [u]E[v]B• (a) Is (, )…

A:

Q: The Gram-Schmidt process transformsthe basis u1=(-3,1), u2=(7, 1) of R´ into the orthogonal basis…

A: Orthogonal set problem....

Q: The Gram-Schmidt process transforms the basis u1=(-1, 2), uz=(6, –2) of R into the orthogonal basis…

A:

Q: Find the matrix for T relative to the basis B, and use Theorem 8.5.2 to compute the matrix for T…

A:

Q: Let B'- {1+2x, 3-x} And B = {1,x} be Basis for Pi a) s Find the Transilion matrır Pine from B' toB…

A:

Q: Let {u₁, U2, u2} be an orthonormal basis for an inner product space V. Suppose v = au₁ + bu₂ + cuz…

A: We have v=au1+bu2 +cu3 Now, ∥v∥=a2+b2+c2 Given ∥v∥=80 So,  80=a2+b2+c2⇒802=a2+b2+c2⇒80=a2+b2+c2…

Q: The Gram-Schmidt process transforms the basis u=(1,2), u2=(2,-6) of R into the orthogonal basis…

A:

Q: Use the Gram-Schmidt process to transform the given basis {w1, W2, W3} into an orthogonal basis…

A:

Q: The Gram-Schmidt process transforms the basis u=(1, 2), u2 =(6, 2) of R² into the orthogonal basis…

A:

Q: 5. (a) Show that the vectors u1 = (3, 1,0), u2 = (-1,3,0) and uz = (0,0, 4) form an orthogonal basis…

A:

Q: 6. Define fe (R2)* by f(x, y) 2x + y and T: R2 (3x + 2y, x). (a) Compute T'(f). (b) Compute [T']p,…

A: We will use the basic knowledge of linear transformations to answer all the three given subparts of…

Q: Answer the following questions about the Gram-Schmidt process for obtain- ing an orthogonal basis…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: 2. Consider the set (a) Verify that this is an orthogonal basis of R³. (b) Write the vector v = as a…

A:

Q: Let B = (1, x + 2, (* – 1)", 9x) be an ordered basis for Pg. Find the coordinate vector of f(æ) = 8a…

A: Answer

Q: =,4} is linearly dependent. 2, V3). 3 000- 2 3 5. undant vector of R³ (b) {1, ₂} is linearly indepe…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.