(11 Let u Show that B } is an orthogonal basis of R3. (b) Convert B into an orthonormal basis C of R3 by normalizing ü, ū and w. Show your work. Find the change of coordinates matrices Psee and Pee-swhere C is the or- thonormal basis of R3 you found in (b) and S is the standard basis of R3. Justify your answers. Suppose now that ü, ū and w are eigenvectors of a 3 x 3 matrix A...
1. Show that {ū1, ū2, ū3} is an orthogonal basis for R3, and write ž as a linear combination of the vectors {ū1, ū2, ū3}, 1 ū1 -[:] -2 -2 ū2 = [ ] ū3 = Ž -11 -3 -17
Please show work and explain. Suppose A is the matrix for T: R3 R3 relative to the standard basis. Find the matrix A' for T relative to the basis B': 3 -1 -2 4 A= 1 5 B' = {(1,1, -1),(1,-1,1),(-1,1,1)}
Suppose A is the matrix for T: R3 → R3 relative to the standard basis. Find the matrix A' for T relative to the basis B': 3 -2 A 4 2 5 B' = {(1,1, -1), (1,-1,1),(-1,1,1)}
Find an orthonormal basis for the subspace of R3 spanned by Extend the basis you found to an orthonormal basis for R 3 (by adding a new vector or vectors). Is there a unique way to extend the basis you found to an orthonormal basis of R3 ? Explain.
Question 15: Do the vectors below form a basis for R3? If so, explain. If not, remove as many vectors as you need to form a basis and show that the resulting set of vectors form a basis for R3. -- () -- () -- ().- 0 1
QUESTION 3 Let S = {(6, 0, 3),(0,5,5),(0,1,0)} be an ordered basis of R3. Let v be a vector in R3, v=(4,7,-1) You calculate V in the basis of S. And get: (a1, a1, a3) What is the value of a3?
Suppose T: R3–M2.2 is a linear transformation whose action on a basis for R3 is as follows: 0 -7 -7 -10 -10 T]01- T TI? 2 2 -7 -6 -10 -9 0 1 Give a basis for the kernel of T and the image of T by choosing which of the original vector spaces each is a subset of, and then giving a set of appropriate vectors. Basis of Kernel is a Subset of R3 Number of Vectors: 1 Bker...
Determine if the set of vectors shown to the right is a basis for R3. If the set of vectors is not a basis, determine whether it is linearly independent and whether the set spans R3 A. The set is linearly independent B. The set spans R3. C. The set is a basis for R3 D. None of the above are true.
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector v in the orthogonal complement of the space 0 Span 2,2 Do not simply compute the cross product. (c) Let A be a 5 × 2 rnatrix with linearly independent columns. Using the rank-nullity theorem applied to AT, and any other results from the course, find the dinension of Col(A) 2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector...