An orthogonal basis for the column space of matrix A is (V₁, V₂, V3). Use this orthogonal basis to find a QR factorization of matrix A. Q=.R= (Type exact answers, using radicals as needed.) A= 1 -1 0 1 1 25 -2 1 23 42 48 V₁ = I 1 0 1 V₂ = 1 2 1 V3 = 3 3 0 -3 3

Let A be a 3x3 matrix such that Assume that the vector V = E -2 is a solution of the matrix equation 3 Enter the vector V₁ in the form [C₁, C2, C3]: -12 12 -24 Find three vectors V₁, V₂, V3, different from V, which are also solutions of this equation. Enter the vector V₂ in the form [C1, C2, C3]: Nul (A) = Span (3) ED Enter the vector V3 in the form [C1, C2, C3]: Ax=

An orthogonal basis for the column space of matrix A is {v1, v2, V3). Use this orthogonal basis to 2 5 find a QR factorization of matrix A. -1 -2 1 2 A= 4 3 V, = V2 = 4 1 6 2 1 2 1 6 8 1 Q=DR=D (Type exact answers, using radicals as needed.)

Describe all least-squares solutions of the equation Ax = b. 重 110 1 110 b 10 1 A = 101 12 The general least-squares solutions of Ax = b for the given matrix A and vector b are all vectors of the form x =+x (Simplify your answers.) with x, free.