Let B = 3 -5 be an orthogonal basis for R³ and let V = 2 e B-coordinated [V] of V. 20 [ ] -13

Q: The set B = {1-1², 2t-12², 1-1-1²) is a basis for P2. Find the coordinate vector of p(t) = 3 +…

A:

Q: Find a basis for the plane 4 + 3y + 5z = 0 in R. %3D

A:

Q: Let b = (2, -4, 2). Let W be the hyperplane b-. (a) What is the dimension of W? (b) Find a basis for…

A:

Q: the basis of P2 cons tive to B.

A: Introduction: For some n, consider V to be a subspace of Rn. A basis for V is a collection of…

Q: The set F = {1+t,t +t, 1+2t+t2} is a basis for P₂. Find the coordinate vector of p(t)= 3 +t-4t²…

A:

Q: The set B={1-1², -2t-t², 1-t-t²} is a basis for P₂. Find the coordinate vector of p(t)= -3-11t-2t²…

A:

Q: Let B = O If the coordinate representation of the vector in the basis B is representation of 7 in…

A:

Q: Let B = vector of 7 = E [V]B 0 1 00 {[%] [83] [28] [89]} 9 9 relative to B. -5 -2 || be an ordered…

A:

Q: The set B is a basis for R². Find the coordinates of the vector [Z] B 9. -10] relative to the basis…

A:

Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: 2

A:

Q: The vectors V, -5 [29] 24 [04.0₂ Write span R2 but do not form a basis. Find two different ways to…

A:

Q: Let B = (1, t + 8, (t – 1)², 4t° ) be an ordered basis for P3. Find the coordinate vector of P(t) =…

A:

Q: 1. Show that the vectors (1, 1,0), (1, 1, 1) and (1,0, 0) are a basis of R3. Find the coefficients…

A:

Q: Let ----0-- -2 = Show that {V₁, V2, V3} forms an orthogonal basis in R³. Express W= as a linear…

A:

Q: Let [3³] Ai B , where B = {b₁,b₂} is a basis in R². Then 3 B 061+06₂

A:

Q: Show that {u₁, u2} is an orthogonal basis for R². Then express x as a linear combination of the u's.…

A: Given:u1​=[2−6​],u2​=[124​],x=[2−2​]  Step 1: Check OrthogonalityTwo vectors u1​ and u2​ are…

Q: 6. Verify that S is an orthogonal basis for R³. Use this to write u as a linear combination of the…

A:

Q: 5. Let V = {(a, b, c, d): a + 3b-2c=0}. Show that (-3, 1, 0, 0), (2,0, 1, 0), and (0, 0, 0, 1) form…

A: 5) Given  that  Let, So we have  .Hence Noted that .Because  Hence basis for subspace V of  is

Q: Find the coordinate vector of v = [-7 [-7 [011], [221] ). −4 -4 -5] relative to the ordered basis B…

A: Vβ​=[−3​0​−2​]   Explanation:

Q: 1) Write v as a linear combination of the orthogonal basis V₁,...,V using dot products: V= |; V₁ =…

A: The given vectors are v=23, v1=45, v2=-54

Q: In R3, let S be the set of vectors 3 S = {V1, V2, V3, V4} = -3 -2 -4 -4 a. Explain why S spans R³…

A:

Q: The vectors : 1 3 5 2 = = 11 --8-8-6 = 0 7 form a basis for R³ if and only if k k

A: Given vectors form basis for R^3 iff when k=21.Explanation:Three vectors from R3 from basis for  R3…

Q: Consider two bases B = {b1,b2} andC : such that bị = cq – 4c2 and b2 = 6c1 – 5c2. Find the…

A: