Given the set V = R².

the addition condition of 2 objects in V is described as : u(x, y) and v(x', y') are in V,  u + v = (x, y) + (x', y') = (x + x' + 6, y + y')

Determine whether the following vectors are dependent or independent?

V1 (1, 2, 5, 3)

V2 (2, -1, 5, 4)

V3 (2, -1, 4, 1)

V4 (2, 4, 1, 0)

Determine the value(s) of "t" for which the set S = {V1, V2, V3} form a basis for R³

V1 (-1, 13, 9)

V2 (0, 15, 1)

V3 (1, 0, t)

Let U(9, -3, -3), V(-4, 8, -3), and W(6, 7, -1).

calculate the scalar triple product U.(VxW)

Let A the standard matrix of a rotation of θ = π/3 followed by a reflection about y-axis.

A =

find a21

Find the area of the triangle ABC. A(2, 2, 1),  B(-4, 3, 3) and C(2, -9, 4)

Find the norm of the image of U(6.1, 5) by an orthogonal projection on x-axis

Find the norm of the image of U(3, 5.8) by an reflection about x-axis