a) Given the rotation matrix 1 R=0 -1 0 1 find the unit vector ô and 0 E [0, T] such that el@]@ = R. %3D

Q: Find a unit vector orthogonal to both u and v. u = 8i – 16j + 2k v = 16i + 32j – 6k -

A: In the given question we have to find the unit vector orthogonal to both u and v. u=8i-16j+2k…

Q: 6. Consider the vectors u = (1,–2), v = (4,3), and w = (9,4). Find scalars k and k2 such that w =…

A:

Q: Consider the two bases B = {b₁,b2} and C = {₁, 2} for R² where 3 5 = = - [B]-4-[13] 4-[8]), 4-[8] =…

A:

Q: Find the vector pointing in the direction opposite that of (6, –8) with length 20.

A: The given vector  6,-8 For a given vector v, to find a unit vector u in opposite direction of v…

Q: Let the rotation matrices be in each of the axes 1. R. 0 cos 0 - sin 0 0 sin0 cos 0 cos 0 0 sin 0 Ry…

A: We will find out the required position of vector (7,4,1) after the rotation.

Q: 1. Find an orthogonal basis for the span of the set S in the vector space V. a. {(6,-3,2), (1, 1,…

A:

Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

Q: c) Write the 3D Rotation Matrix around the z-axis by 0 = 45°: Rows: 1 Columns: 1

A:

Q: Find the matrix A of the linear transformation T from R? to R² that rotates any vector through an…

A:

Q: 2. Give the matrices of the following plane transformations: a)The rotation around the origin of the…

A: (b) Given the horizontal transvection Te2=-3e1+e2. This is followed by a reflection with respect to…

Q: Let Re:R → R² is a linear transformation rotation function, where 0 is an angle of th Гcos ® -sin 0…

A: This is a problem of linear transformation.