Let (a, b, c) be the vector orthogonal to (-2, 1, 5).
Then -2a+b+5c=0.
If we take a=2, b=-1, c=1 then (-2)×2+1×(-1)+5×1=0.
Hence (2, -1, 1) is orthogonal to (-2, 1, 5).
(a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal projection of the vector (1,-3) on the vector v- (-1,5). 2 marks] (c) Using your result for part (b) verify that w = u-prolvu is perpendicular to V. 2 marks] (a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal projection of the vector (1,-3) on the vector...
Problem 2. Find a vector 7 orthogonal to the row space, and a vector y orthogonal to the column space of the matrix [1 2 1] 2 4 3 [36 4
2) The vector is in the subspace H with a basis B = {1,5}. Find the B-coordinate vector of 3 5x = [-2], 62 = (-). =) Answer:
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector v in the orthogonal complement of the space 0 Span 2,2 Do not simply compute the cross product. (c) Let A be a 5 × 2 rnatrix with linearly independent columns. Using the rank-nullity theorem applied to AT, and any other results from the course, find the dinension of Col(A) 2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector...
(6 points) Find a vector orthogonal to both (-5, -4,0) and to (0, -4, –5) of the form (1,1 -
(a) Find a unit vector that is orthogonal to the plane through the points P(0,0,–3), Q(4,2,0), and R(3,3,1) (b) Find two non-parallel vectors that are orthogonal to the vector Ŭ = i + 2) + 3k (c) Find the angel between the vector Ở = 51 + 21 – k and the z - axis (d) Describe why it is impossible for a vector to have the following direction angles 511 6 -, B = 3, and y TT π...
I will upvote! (2)()dz in the vector space Cº|0, 1] to find the orthogonal projection of f(a) – 332 – 1 onto the subspaco V (1 point) Use the inner product < 1.9 > spanned by g(x) - and h(x) - 1 proj) (1 point) Find the orthogonal projection of -1 -5 V = 9 -11 onto the subspace V of R4 spanned by -4 -2 -4 -5 X1 = and X2 == 1 -28 -4 0 -32276/5641 -2789775641 projv...
Let L be the line passing through the point P(1,5, -2) with direction vector d=[0,-1, 0]T, and let T be the plane defined by x–5y+z = 22. Find the point Q where L and T intersect. Q=(0,0,0)
Given the orthogonal basis B for R4 and the vector v below, find the Fourier coefficients for v with respect to B. Your coefficients should be given in the same order as the vectors in B. B = 1 22 -1 | 7 | 0 | 0 | |-1 | 2 Fourier Coefficients: 0, 0, 0, 0
Find a vector that is orthogonal to u = -2i+ 5j - 3k and w = 3i+2j+k.