6. Let P be the subspace in R 3 defined by the plane x − 2y + z = 0. (a) [5 points] Use the Gram–Schmidt process to find orthogonal vectors that form a basis for P. (b) [5 points] Find the projection p of b = (3, −6, 9) onto P. 6. Let P be the subspace in R3 defined by the plan 2y+z0 (a) [5 points] Use the Gram-Schmidt process to find orthogonal vectors that form a basis...
20 3. Let 1 = 2 and = 5. Let W = Span{11, 13). (a) Give a geometric description of W. (b) Use the Gram-Schmidt process to find an orthogonal basis for W. (c) Let = 2 Find the closest point to į in W. (a) Use your orthogonal basis in part (b) to find an orthonormal basis for W.
11 1 4 15 2. let A lo 1 -9 1 3 7 (a) Explain how would you find a basis for the column space of A. (b) Use the Gram-Schmidt process to produce an orthogonal basis for Col A.
) Let A be the following matrix: 13 0 2 0 2 2 0 0 6 (a) Enter its characteristic equation below. Note you must use p as the parameter instead of , and you must enter your answer as a equation, with the equals sign. (b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24. 5 (c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal...
3. Consider the following vectors, where k is some real number. H-11 Lol 1-1 a. For what values of k are the vectors linearly independent? b. For what values of k are the vectors linearly dependent? c. What is the angle (in degrees) between u and v? 4. Here are two vectors in R". Let V = the span of {"v1r2} a. Find an orthogonal basis for V (the orthogonal complement of V). b. Find a vector that is neither...
3 The two vectors X1 = 0 -1 8 X2 = 5 -6 form a basis for a subspace w of Rº. Use the Gram-Schmidt process to produce an orthogonal basis for W, then normalize that basis to produce an orthonormal basis for W.
Entered Result Messages Answer Preview incorrect You have entered vectors which are not 1-1 orthogonal 0 0 incorrect incorrect At least one of the answers above is NOT correct. 2 of the questions remain unanswered (1 pt) 1210 Let A = 341-2 Find orthonormal bases of the kernel, row space, and image (column space) of A Basis of the kernel Basis of the row space Basis of the image (column space)
5. (10pts) Let B (v1 (1,1,0), v2 (1,0,-1). v3 (0,1,-1)) be a basis of R3 Using the Gram-Schmidt process, find an orthogonal basis of R3. (You don't have to normalize the vectors.)
Please show the detail, thank you! (1 point) (a) Let -4 -7 -2 -4 V1 = and V2 = 1 6 0 2 and let W = span{V1, V2}. Apply the Gram-Schmidt procedure to vi and V2 to find an orthogonal basis {uj, u2 } for W. uj = U2 = -13 2 (b) Consider the vector v = - Find V' E W such that || V – v' || is as small as possible. 15 8 V =...
(3 points) Let 4 2 -4 -13 0.5 2 4 0 4.5 Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R4 spanned by x, y, and Z. (3 points) Let 4 2 -4 -13 0.5 2 4 0 4.5 Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R4 spanned by x, y, and Z.