(1 point) The set >-{[12][13) 45 is a basis for R2. Find the coordinates of the...
Problem 6 A bilinear pairing on R2 is given on basis vectors by <ei, ei >= 13; <ei, e2 >=< e2, ej >= 7; <e2,e2 >= 26 a) [3 pts) Find the matrix representation of the pairing. b) (4 pts) Explain why the bilinear pairing defines an inner product. c) [3 pts) If v = [5 – 3]T, find a non-zero vector w with < v, w >= 0
1 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi for a. r> 0 and 0 << 271 p < 0 and 0 < < 271 )
(a) Find Cartesian coordinates for the polar point (-1, -1) and plot the point. (b) Find Polar coordinates with r > 0 and -1 < <a for the Cartesian point (-1, V3) and plot the point. (c) Convert the equation x2 + y2 = x to polar form and sketch the curve. (d) Convert the equation r = 5 csc @ to Cartesian form and sketch the curve.
Find the rectangular coordinates for the point whose polar coordinates are given. 8 TT 6 (x, y) = ) =( Convert the rectangular coordinates to polar coordinates with r> 0 and 0 se<2n. (-2, 2) (r, 0) Convert the rectangular coordinates to polar coordinates with r> 0 and O So<211. (V18, V18) (r, ) = Find the rectangular coordinates for the point whose polar coordinates are given. (417, - ) (x, y) =
5. (10 pts) Use the inner product < x,y > = 22191 +2242 in R2 and the Gram - Schmidt process to transform {(2, -1), (-2, 10)} into an orthonormal basis
Part (b) only, The Cartesian coordinates of a point are given. (a) (-6, 6) (i) Find polar coordinates (r, 0) of the point, where r> 0 and 0 5 0 < 21. (6, 6) = ( 6v2, 37 (ii) Find polar coordinates (r, O) of the point, where r<0 and 0 S 0 < 21. (5, 6) = ( -622, 71 (b) (3,3V3) (i) Find polar coordinates (r, 0) of the point, where r>0 and 0 = 0 < 21....
Find i (Assume vs = 18 V.) + OVO Us I + + 2 V >5 kΩ
Find the equation of the plane 2 Find the equation of the plane containing the point (1,0,4) (1,0,4) and normal to the 52,','> Vector
Find the length of spiral curve T() = ----- 0 < > < 2”
Solve the IVP 1 (31= [ -> ] (3) [6**) (O)= [-] +