(1 point) -4 Let L be the line spanned by 0 in R Find a basis of the orthogonal complement L1。L Answer:
(1 point) Let L be the line spanned by in R4 Find a basis of the orthogonal complement L' of L.
2. Find the closest point to y = in the subspace H = Span [ o། [ 17 [10] 3. Let B = {| 2 |,|-2, 1}. Find the coordinate vector of x = [1] relative to the [=1] [4] [2] orthogonal basis B for R3. ངོ- v1cs None of the above 5. Which of the following is true about the sets of vectors S and T? 3 1 [3 ] , 2 ), T={l U L-13] The set S...
Let W = span{ (-2, 1; 2,0), (4,0-5, 2)] the Groun - Student Produrt to find an enthonormal basis for W The dimension of wt, the orthogonal complement of w.is basis from (a), either before or after normalizing projw (1,1,1,). be your to find
4 4. Here are two vectors in R". Let V - the span of fv,v,). a. Find an orthogonal basis for V (the orthogonal complement of V). You get an extra point for expressing your basis as vectors with integer components. b. Find a vector that is neither completely in V, nor completely in c. Find a vector in V which is a unit vector.
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...
1 4 3 13 The vectors V1 = | 2 and V2 = 5 span a subspace V of the indicated Euclidean space. Find a basis for the orthogonal complement vt of V. 8 36 4 13 Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. A basis for the orthogonal complement vt is {}. (Use a comma to separate vectors as needed.) OB. There is no basis for the orthogonal...
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.
Let W Span((2,-3,0, 1), (4,-6,-2, 1), (6,-9,-2,2) R4. (a) Find a basis for W (b) Find a basis for W (c) Find an orthogonal basis for W and W (d) The union of these two orthogonal bases (put the basis for W and W what? Why is the union orthogonal? into one set) is an orthogonal basis for
Let W Span((2,-3,0, 1), (4,-6,-2, 1), (6,-9,-2,2) R4. (a) Find a basis for W (b) Find a basis for W (c) Find...
Problem 3 Let L: R4 → R3 be given by L (6)-1 (3:01 - 4.12 + 1104) (15.12 + 9.23 - 21:04) 6.01 +9.12 + 4.13 - 5.14) a) (4 pts] Show that L is a linear transformation, and find the matrix representation A of L with respect to the standard bases for R' and R3. b) [3 pts] Use part a) to find a basis for ker(L). c) [3 pts] Use part a) for find a basis for im(L).