Problem 9. Determine if the following pair of vectors are orthogonal. -3 13 -3 0 -7'0...
orthogonal vectors answer says 3. (5/13,12/13) and 4. (-1/5,6/5) but i dont see why. both please! Find a unit vector orthogonal to (12,-5). Are there any other than the one you found? 3. = (-7,8 ) , find a vector p such that u and p are orthogonal and 4. For the vectors u = (6,1) and p-11
Question 6) (9 points) Prove each of the following statements. (a) Suppose that the vectors {v, w, u} are linearly independent vectors in some vector space V. Prove then that the vectors {v + w, w + u,v + u} are also linearly independent in V. (b) Suppose T is a linear transformation, T: P10(R) → M3(R) Prove that T cannot be 1-to-1 (c) Prove that in ANY inner product that if u and w are unit vectors (ie ||vl|...
3. Given pairwise orthogonal vectors u, v, w ER(each vector is orthogonal to every other), with || || = ||0|| = ||w|| = 1, and C1, C2, C3 € R, prove that || Cu + c2v + c3w||2 = cſ + cx+cz.
1- 2- 3- 1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors and w - -3 4 9 be a vector in subspace W, where W = Span{u, v, w}. Let y= 11 -27 Write y as a linear combination of u, v, and uw, i.e. y = ciu + cqũ + c3W. Answer: y=
Determine whether each of the following statements are true or false, where all the vectors are in R". Justify each answer. Complete parts (a) through (e) a. Not every linearly independent set in R" is an orthogonal set. OA True. For example, the vectors are linearly independent but not orthogonal OB. True. For example, the vectors are linearly independent but not orthogonal. O O C False. For example, in every linearly independent set of two vectors in R. one vector...
Determine which of the following set of vectors are orthogonal. 20 -201 20 V = (13)= 0 20 20 20 20 V only U only Neither U and V
#13 In Problems 9 21, determine whether the given set of vectors forms a basis for the specified vector space. IR 12 IR 5'8 13 0 16 IR 0 15 IR3 18 17 IR 19 IR
26 or 28 or both 25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of which is projyu. Insum of two orthogonal vect as a sum of two 26. (3.-7),2, 6) 27, u(8, 5), v 28, 2, 8), v-(9,-3 29 and 30, find the interior angles of the triangle with 25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of...
Determine all vectors v that are orthogonal to u = (9,-4.0). Ov =(81,97,t), where is any real numbers o v = (47.91,t), where is any real numbers v=(4t, 11t,s), where s and are any real numbers v=41,97,5), where s and are any real numbers Ov=(8t, 11t,s), where s and are any real numbers