We will continue to work on the concepts of basis and dimensions in this homework Again, if neces...
2. Linear dependence of vectors: If we want to describe any vector in three dimensions, we need a basis of three vectors, and we usually choose i,j. k, the unit vectors in the r, y, z directions. We could equally well have chosen for example a = i+5, b = i-j and c = i+2] _ k. Then the vector v = 41+2] _ k would be expressed as v = 3a + )b-c a, b, c form a suitable...
Problem 4. Let n E N. We consider the vector space R” (a) Prove that for all X, Y CR”, if X IY then Span(X) 1 Span(Y). (b) Let X and Y be linearly independent subsets of R”. Prove that if X IY, then X UY is linearly independent. (C) Prove that every maximally pairwise orthogonal set of vectors in R” has n + 1 elements. Definition: Let V be a vector space and let U and W be subspaces...
only a-i T or F
lit khd where it came from 4. You do not need to simplify results, unless otherwise stated. 1. (20pts.) Indicate whether each of the following questions is True or False by writing the words "True" or "False" No explanation is needed. (a) If S is a set of linearly independent vectors in R" then the set S is an orthogonal set (b) If the vector x is orthogonal to every vector in a subspace W...
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...
When dealing with standard vectors (with purely real elements) we are used to finding the angle between the vector from But what happens when we are dealing with vectors that have complex elements. In quantum mechanics, in general, the inner product is a complex number, which does not define a real angle The Schwarz Inequality helps us in this regard However, according to it, the only thing we can know is that the absolute value of the inner product is...
It's saying A, D and E wrong but was pretty sure that was
answer
(1 pt) The dot product of two vectors and y Yn TI in R" is defined by - y = 1Y1 + X2Y2 + . ..+ xnyn The vectors and y are called perpendicular if x y = 0 6 8 Then any vector in R perpendicular to -9 can be written in the form (1 pt) All vectors are in R Check the true statements...
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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. Recall that y |I 1lcos 0, for any two vectors and y with angle that in mind, as long as f is differentiable at a fixed point ã, we can write between them. With Since is a unit vector, we can rewrite this as V/(a)ll cos(0) For what values of θ is this value maximized? Minimized? How do we choose u to achieve these values of 0?
3. Recall that y |I 1lcos 0, for any two vectors and...
Problem 4. Let V be the vector space of all infinitely differentiable functions f: [0, ] -» R, equipped with the inner product f(t)g(t)d (f,g) = (a) Let UC V be the subspace spanned by B = (sinr, cos x, 1) (you may assume without proof that B is linearly independent, and hence a basis for U). Find the B-matrix [D]93 of the "derivative linear transformation" D : U -> U given by D(f) = f'. (b) Let WC V...
can anybody explain how to do #9 by using the theorem
2.7?
i know the vectors in those matrices are linearly independent,
span, and are bases, but i do not know how to show them with the
theorem 2.7
a matrix ever, the the col- ons of B. e rela- In Exercises 6-9, use Theorem 2.7 to determine which of the following sets of vectors are linearly independent, which span, and which are bases. 6. In R2t], bi = 1+t...