
2) Fe the nullspace, PA is spanned by 3 linearly independent vectors, and Aºis 5x7,' what...
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
0/1 pts Inooreat Question 9 Suppose W is a subspace of R" spanned by n nonzero orthogonal vectors. Explain why WR Two subspaces are the same when one subspace is a subset of the other subspace. Two subspaces are the same when they are spanned by the same vectors Two subspaces are the same when they are subsets of the same space Two subspaces are the same when they have the same dimension Incorrect 0/1 pts Question 10 Let U...
2) Given 3 vectors. 11 | u = 0 | u = -1 L2 a) What vector space do these vectors belong to? b) Geometrically describe the space spanned by vectors uj and u2. c) Is vector, v, in the subspace spanned by the vectors uj and u2? d) Are all 3 vectors linearly dependent or independent of each other? Explain why or why not. e) If possible, find the linear combination of vectors u; and uz that equals vector...
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...
ts) Find three linearly independent characteristic vectors and all characteristic roots of the matrix 3 2 -3 -3 -4 9 1-1 - 5
1) Determine if w is in the subspace spanned by v1, v2,
v3
2) Are the vectors v1, v2, v3 linearly dependent or
independent? justify your answer
Question 2. (15 pts) Let vi=(-3 0 6)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer
a and b
Are the following vectors linearly independent? 7 (a) ai = (*) 3 2 02 03 12 10 9 6 (12) 0 0 (b) di = A2 = 03 = 0 0
(1 point) Find a linearly independent set of vectors that spans the same subspace of R3 as that spanne -3 3 3 2 -5 -2 4 0 Linearly independent set:
4. Consider 3 linearly independent vectors V1, V2, V3 E R3 and 3 arbi- trary numbers dı, d2, d3 € R. (i) Show that there is a matrix A E M3(R), and only one, with eigenvalues dı, d2, d3 and corresponding eigenvectors V1, V2, V3. (ii) Show that if {V1, V2, V3} is an orthonormal set of vectors. then the matrix A is symmetric.
Are these vectors linearly independent? • [3 4 0 2],[4 − 2 6 14],[0 8 − 6 − 11]