,
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...
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
ote: The norm of is denoted by |vand is calculated N a vector u Consider a subspace W of R4, W span(1, v2, v3, v4)). Where 0 из- 1. Find an orthonormal basis Qw of W and find the dimension of W 2. Find an orthonormal basis QWL of WL and find the dimension of WL 3. GIven a vector u- . find the Qw coordinate of Projw(v) . find the Qwa coordinate of Projwi (v) » find the coordinate...
(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.
Consider the subspaces U=span{[4 −2 −2],[10 1− 4]} and W=span{[3 −4 −1],[10 2 −2]}.Find a matrix X∈V such that U∩W=span{W}.
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.
Question 1 Question 2 Let u, v, w be three vectors in R4 with the property that 4u - 30+2w = 0. Let A be the 4 x 2 matrix whose columns are u and u (in that order). Find a solution to the equation Ac =W. Let 1 -2 0 3 A=1 -2 2-1 2 -4 1 4 Find a list of vectors whose span is the set of solutions to Ax = 0. 1 1 Enter the list...
5 3 1 0 Problem 10 Let wi = ,W2 W3 Let W = Span{W1,W2, W3} C R6. 11 9 1 2 a) [6 pts] Use the Gram-Schmit algorithm to find an orthogonal basis for W. You should explicitly show each step of your calculation. 10 -7 11 b) [5 pts) Let v = Compute the projection prw(v) of v onto the subspace W using the 5 orthogonal basis in a). c) (4 pts] Use the computation in b) to...
ww-{) [:]}------ Let W =Span 2 1. and suppose the vectory is in W . Find all possible values of r and y. Enter x value(s) in the first blank and y value(s) in the second blank provided. Blank # 1 Blank # 2
... Let v = , u = , and let W the subspace of R4 spanned by v and u. Find a basis of W .