Use the Gram-Schmidt process to find an orthonormal basis for Span ([2, 1, 2, 4], [0,-1, -2,01¹).

Find the coordinate matrix of x relative to the orthonormal basis B in R". x = (10, 20, 5), B = {G) (-), (0, o, 1)} [x]g = 1 1

Use the Gram-Schmidt process to find an orthonormal basis for im(A), where 1 7. A = 1 1 -2 122,

suppose that x↓1,..,x↓(n-1) are linearly independent vectors in R^n and also x↓n is notin the span of x↓1,..,x↓(n-1) . 1. prove that x↓1,...,x↓n is a basis of R^n. 2. Prove that if x↓(n+1)∈R^n, then x↓1,..,x↓n,x↓n+1 are not linearly independent