1. (- Let W₁ --E--E) and W₂ = = 1 -1 (a) Find a basis for W₁ W₂. What is dim(W₁ W₂)? (b) Show that R³ =W₁ + W₂. (c) Find a subspace U such that R³ = W₁ OU. be given subspaces of R³.

Q: With T defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: The given matrix  and the vector  and  is defined by .The aim is to find the vector  whose image…

Q: Find the change-of-coordinate matrix P from B to C and P from C to B for the bases B = {1,t,t^2} and…

A: Let U={u1,u2,⋯,un} and V={v1,v2,⋯,vn} are two bases of a vector space W.The identity map I:W→W…

Q: Find a basis for the subspace of R° spanned by the following vectors. 6. 18 -3 -3 6 6. -18 -18 14…

A: We solve this by row reduced echolon  form

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

Q: V= घ X, xz LX4 :-X₁ + 2x₂ + −X₂ + 4xy=0 and x₁ + 3x₂ -X₂ - 2xy = 0 Show that V is a subspace of Ru…

A:

Q: 2. The vector x = vector [x]B A 1 3 0 = [1] a [9] in R2 relative to the orthogonal basis B = What is…

A: