3.4.22 vii 21 Find the Gram matík of the vectors () 0) (0) Find the Gram...
3. 17 pts] (a) Perform the Gram-Schmidt process on the following vectors to find an orthonormal basis: (b) Construct the QR decomposition of the following matrix: L-2I (c) What is the rank of the matrix?
6. Find the matrix P that projects vectors in R4 onto the column space of each matrix. 2 1 [BB]A= 1-21 0 1 (b) A= | 0 1 1 -1 (a) 1131 0101 1011 1231 1112 6. Find the matrix P that projects vectors in R4 onto the column space of each matrix. 2 1 [BB]A= 1-21 0 1 (b) A= | 0 1 1 -1 (a) 1131 0101 1011 1231 1112
linear algebra (a) Use Gram-Schmidt, (using the given vectors as labeled) to find an orthonormal basis for the span of 0 0 V3- (b) Use Gram-Schmidt, (using the given vectors as labeled) to find an orthonormal basis for the span of 0 V3-0 v2= (c) What can we conclude from the two examples computed above? Also, did you find one computation "easier than the other? If so, what do you think made it easier?
22. (a) Find two vectors that span the null space of A 3 -1 2 -4 (b) Use the result of part (a) to find the matrix that projects vectors onto the null space of A. (c) Find two orthogonal vectors that span the null space of A. (d) Use the result of (c) to find the matrix that projects vectors onto the nul space of A. Compare this matrix with the one found in part (a). (e) Find the...
Tk 1 21 5 -5 k (a) Find the determinant of A in terms of k (b) For which value(s) of k is the matrix A invertible? (c) Let B-(k,1,2,0), (0, k, 2,0),(5,-5, k,0)) be a set of vectors in R4, and let k equal some answer you gave for part (b) of this question. Add an appropriate number of vectors to B so that the resulting set is a basis for R' Tk 1 21 5 -5 k (a)...
0 2 4. [6 pts) (a) (4pts) Find a basis for the span of vectors ui -2 | u,-|-1 | , and u3 | 5 ,u2 = 0 (b) (2 pts) Find the rank and nullity for the matrix A-u u us].
How can I get the (a) 3*2 matrix A? x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
The given vectors form a basis for a subspace W of ℝ3. Apply the Gram-Schmidt Process to obtain an orthogonal basis for W. (Use the Gram-Schmidt Process found here to calculate your answer.) x1 = 1 1 0 , x2 = 3 4 1
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...
Question 4 (2 points) After applying the Gram-Schmidt algorithm to the vectors L1 = (3, 0, 3, 0), 2 = 1, 1,0, 0), 3 = : 0, 1,t, 1) (precisely in this order) where t is a parameter, one obtains an orthogonal basis {w1, w2, w3} of the subspace in R4. What is the last vector w3 obtained by the Gram-Schmidt algorithm? t, -9 27 t, 9 27 (ਉ - ੮, ਮੰਗ - 1) (ਸੰਨ + ਕt, + ਕt, +...