Question 1 Question 2 Let u, v, w be three vectors in R4 with the property...
linear alegbra Let u, v, w be linearly independent vectors in R3. Which statement is false? (A) The vector u+v+2w is in span(u + u, w). (B) The zero vector is in span(u, v, w) (C) The vectors u, v, w span R3. (D) The vector w is in span(u, v).
Given the following vectors u and v, find a vector w in R4 so that {u, v, w} is linearly independent and a non- zero vector z in R4 so that {u, v, z} is linearly dependent: 1-3 8 -8 -2 u = V= 5 -4 10 0 w=0 1- z=0 0
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...
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
Let u = [1, 3, -2], v = [-1, 1, 1], w = [5, 1, 4]. a) Check if the system of vectors {u,v,w} is an orthogonal or othonormal basis of E3. b) Find the coordinates of the vector [1,0,1] in this basis.
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=
question 3 (b) Problem #3: Let R4 have the inner product <u, v>-#1v1 + 2112v2 + 31/3V3 + 414V4 (a) Let w (0, 6, 3,-1). Find |w (b) Let Wbe the subspace spanned by the vectors u (0, 0, 2,1), and u2-,0,,-1) Use the Gram-Schmidt components of the vector v2 into the answer box below, separated with commas process to transform the basis fui. u2 into an orthonormal basis fvi, v23. Enter the Enter your answer symbolically as in these...
Previous Problem List Next (1 point) Find a set of vectors {u, v} in R4 that spans the solution set of the equations: x 5x - + y 2y + - W W = = 0 0 - Z u = V =
... Let v = , u = , and let W the subspace of R4 spanned by v and u. Find a basis of W .
Find a basis of the subspace of R4 that consists of all vectors perpendicular to both Problem 11. (12 points) Find a basis of the subspace of R4 that consists of all vectors perpendicular to both Basis: 111 To enter a basis into WebWork, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is was to me, you are » {]J (1) mar yavros en...