(1 point) Let L be the line spanned by in R4 Find a basis of the orthogonal complement L' of L.
4 -5 (1 point) Let L be the line given by the span ofin R3. Find a basis for the orthogonal complement L of L. A basis for L is
Let U be the subspace of R 2 spanned by (1, 2). Find the orthogonal complement U ⊥ of U. Then find a ∈ U and b ∈ U ⊥ such that (0, 3) = a + b.
(5 points) Let 5 -4 v= 1-3 -3 and let W the subspace of R4 spanned by ū and 7. Find a basis of W?, the orthogonal complement of W in R4.
Let L in R 3 be the line through the origin spanned by the vector v = 1 1 3 . Find the linear equations that define L, i.e., find a system of linear equations whose solutions are the points in L. lil (6) Let L in R3 be the line through the origin spanned by the vector v= 1. Find the linear equations that define L, i.e., find a system of linear equations whose solutions are...
(1 point) Let W be the subspace of R spanned by the vectors 27 1 and -7 Find the matrix A of the orthogonal projection onto W. A =
6. Let L be the line in spanned by the vector u =(1,-1,2). (a) (6 points) Compute a basis for the subspace Zt. 7. (6 point bonus! Find the general solution y to the second-order linear differential equa- tion below. Use C.C.C.... for the names of any unknown constants. 0-1 + 424 = 0 (b) (6 points Use the Gram-Schuit process to find an orthonormal basis for L,
Problem 13. Let l be the line in R' spanned by the vector u = 3 and let P:R -R be the projection onto line l. We have seen that projection onto a line is a linear transformation (also see page 218 example 3.59). a). Find the standard matrix representation of P by finding the images of the standard basis vectors e, e, and e, under the transformation P. b). Find the standard matrix representation of P by the second...
Let L in R 3 be the line through the origin spanned by the vector v = 1 1 3 . Find the linear equations that define L, i.e., find a system of linear equations whose solutions are the points in L. (7) Give an example of a linear transformation from T : R 2 → R 3 with the following two properties: (a) T is not one-to-one, and (b) range(T) = ...
Will rate once all is completed. 1) 2) 3) 4) (12 points) Find a basis of the subspace of R that consists of all vectors perpendicular to both El- 1 1 0 and 7 Basis: , then you would enter [1,2,3],[1,1,1] into the answer To enter a basis into WeBWork, place the entries. each vector inside of brackets, and enter a list these vectors, separated by commas. For instance if vour basis is 31 2 and u (12 points) Let...