Let W be the line y = x in R². (a) Find a unit vector u on W. (b) Consider the linear transformation T: R² R² that projects each vector orthogonally onto W. Calculate the matrix for T which is üü¹. (c) Use that matrix to calculate T [1] TH (d) Draw the vector [1] the line W, and the projection T

Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

Q: Let T Find the image of an arbitrary vector V₁ Let T: R² R² be the linear transformation satisfying…

A:

Q: Let l be a line through the origin in R2, Pe the linear transformation that projects a vector onto…

A: Given: l is the line passing through the origin in R2. The linear transformation Pe is defined as…

Q: Write down the 4 x 4 rotation matrix that takes the orthonormal 3D vectors u (Xu, Yu, Zu), V = (xv,…

A:

Q: 2. Now let W be the line y = 2x in R². (a) Find a unit vector u on W. (b) Consider the linear…

A: Dear student as per our guidelines we can solve only first 3 questions. So kindly resubmit remaining…

Q: Consider the vectors u₁ = [1,0,-1], u2 = [1,0,0] and u3 = [0, 1,1], v= [5, 1,3] and w= [1,0,3]. (a)…

A: As per guidelines of Bartleby i am supposed to solve on first three part,if you want more solution…

Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: Let V1 = 1 v2 = V3 = and y = 4 Let W = span {V₁, V2, V3}. Find the orthogonal projection of the…

A:

Q: Calculate the scalar products of the following vectors: 10 1 Q-B 5 W1 -4 9 (a) V₁ = (b) V2 = (c) V3…

A: Note: As per rule I need to solve only first three subparts.

Q: Consider now the transformation T: R² → R² such that a stretch factor of 2 corresponds with the line…

A: Given Information:The black basis is the standard basis of .The red basis  is the basis .The…

Q: Let T be a linear transformation from R° to R². Show that T(0,)=0,, i.e. mapping the zero vector to…

A:

Q: (3) Let L be the line y 2r in the plane. Find a matrix C such hat for every vector H plane, the…

A:

Q: Let T: R2 R³ and u, v E R2 such that T(u) = 1 2 -2 and T(v) = 4 -2 1 Find the image under T of the…

A:

Q: Consider the vectors ā₁ = (-1,2,2), a2 = (2,2, -1), and 3 = (2,-1,2). 1. Compute the projection…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2 Let I be the line in R³ that consists of all scalar multiples of the vector w = -[] 2 Find the…

A: