Please help me with the following questions.

1.

The orthonormal basis of the subspace spanned by the vectors is {} (Use a comma to separate vectors as needed.) 13 The vectors v, = -6 and v2 = 2 form an orthogonal basis for W. Find an orthonormal basis for 6 NO W.The orthonormal basis of the subspace spanned by the vectors is {} The vectors v, = -5 and v2 = 5 form an orthogonal basis for W. Find an orthonormal basis for W. (Use a comma to separate vectors as needed.)Use the Gram-Schmidt process to produce an orthogonal basis for the column space of matrix A. -10 -14 -6 -12 2 0 1 A= - 6 -2 2 - 16 16 16 22 10 2 -2 0 11 An orthogonal basis for the column space of matrix A is {} (Type a vector or list of vectors. Use a comma to separate vectors as needed.)-10 -6 6 0 - 10 4 2 6 6 18 2 4 An orthogonal basis for A, 6 -10 2 -4 , is -6 - 4 6 Find the QR factorization of A with the given orthogonal basis. 16 16 28 22 16 0 6 2 6 6 -6 4 6 The QR factorization of A is A = QR, where Q = and R =Jolt: To find an orthonormal basis for the subspace W spanned by the given rectors, we can use the Gram - Schmidt process. This process takes a set of linearly independent rectors and orthogonalizes them to create an orthogonal or orthonormal bastis. det's start with the rectors v. and v.: 3 12 = 4-67 , V2 = 13 /2 9 / 2 Steps : Normalize v. to get the first rector of the orthonormal basis us : U = VI Il vill in the norm 11 Vill 11 Vill = BE J (4) + 1 - 61 2 + ( 612 1 88 4 / 1Re U, = - 6/ 188 6 / 588 Steph: Find the projection of v, onto u, and subtract it from V. to get a rector orthogonal to U, :proj (vs , Uh ) = ( V. . Us ) x Us 3 4 4 13 / 2 - 6 X - 6 188 188 9/2 6 188 188 4 188 = - 33 X 188 - 6 Now, orthogonalize v. by subtracting the projection. U . = V2 - pry ( V 2 , Us ) 4 3 13 / 2 - 1 - 6 U. = 188 9 / 2 188 3+ 132 88 = 13 - 198 2 88 2 + 198 88 Steps: Normalize U. to get the second rector of the orthonormal basis : = 8 8 ) ( 3 + 138 ) 2 + ( 13 - 198 ) - + 86 ) (9 + 198 1 2 883+ 132 U , = 114211 13 - 198 2 88 2 + 198/ 88 finally, the orthonormal bani's for the subspace I is fuls, 412. Each rector in this bass' will have a length of I and will be orthogonal to the other vector.Sol2: To find an orthonormal basis for the subspace i spanned by the given vectors using the gram-Schmidt process, follows these steps : Given vectors : VI = - 5 V . = I Step1: Normalize v. to get the first rector of the orthonormal basis Us: U 1 = Will in the norm of11Vill = ( 17 + + (-572 + ( H ) - = 142 Now. 1 / 14 2 U, = - 5 / 142 4 / JH2 Steph : Find the projection of is onto us and subtract it from V. to get a vector orthogonal to Up : pro (v2, was ) = ( V2. be ) x 4, 1 / 1 142 1/ 1427 = - 5/ 142 - 5/ 1142 4 / 19 2 1 / 142 = - 59 - 5/142 42542 4 / 542 pro (V2 , 41 ) = - 59 - 5 / 142 42 42 4 / 542 Now, orthogonalize v. by subtracting the projection. &tz = V2 - proj ( v. , U.)1 / 142 Up = - 59 S - 5/ 542 42 1421 G 4 / 542 1 + 59 4254 2 5- 295 42 - 42 16+ 236 42 142 Step 3: Normalize Us to get the second vector of the orthonormal basis : 1+ 59 2 + (5- 295 + ( 6 + 2 3 6 ) H2542 42 142 42 142, Finally the orthonormal basis for the subspace