Consider the matrix A -1 1 0 1 1 1 20-2 1020 2 0 (a) Use the Gram-Scmidt method to find an orthogonal basis for Col(A). (b) Use your basis from (a) to find an orthonormal basis for Col(A).

Need only a handwritten solution only (not a typed one).

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= =₁R=0 (Type exact answers, using radicals as needed.) A = 1 25 -1 -4 1 0 22 1 4 3 1 69 V₁ = 1 1 0 1 1 V2 = -2 ON 0 2 کیا 0 3

Find a basis for the solution space of the given homogeneous linear system. X4- 2x2 + 16x3 = 0 2x, 3x2 + 23x3 = 0 A basis for the solution space of the given homogeneous linear system is { }. (Use a comma to separate vectors as needed.)