Find the coordinate matrix of x relative to the orthonormal basis B in R". x = (10, 20, 5), B = {()(-), (o. o, 1)} [x]g = | 1

-13/27] -4/27 -4/9 5/9 -20/27] -2/27 Let v₁ = √2 = and √3 = Find a vector in IR4 such that -20/27 ' ' -2/9 17/27 4/9 -2/3 2/9 {1, 2, 3, 4} is an orthonormal set. Answer:

A square matrix A is called orthonormal if AT = A-¹. Prove that matrix. Cos 0 sin - sin 0 Cos is an orthonormal

Let L: R3 R2 be defined by the following. X1 + X3 ***] 8x2 Suppose X1 L X₂ P = = 1 -(HH) 4 3 3 1 2 B₁ = 4 ={[8][;}} is an ordered basis for the domain and B₂ = is an ordered basis for the range. Find the matrix representation P for L relative to B₁ and B₂ such that [L(u)]b₂ = P[u]ß₁'

A3) Lat M = (sin(nz): n1,3,5,} Can M form a basis for L'(0, n)?