Sketch a diagram of the linear map G that maps the rectangle R = [0, 1]×[0, 1] in the uv-plane to the parallelogram P in the xy-plane with vertices (0, 0),(2, 2),(1, 4), and (3, 6). Draw the rectangle in the uv-plane on the left and its image P in the xy-plane on the right, with an arrow labeled G in the middle.  Find the map G(u, v) = (x(u, v), y(u, v)) explicitly.  Set up, but do not evaluate an integral in u and v to calculate Z ZRxy dA

Q: Let y = proj₁y = 3 -2 and u = -3 (a) Find the orthogonal projection of y onto u. 2 1 = (b) Compute…

A: Here we have to find orthogonal projection of y onto u and also we have to calculate distance d.

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: Show that the line [x, y, z]= [5,-1,3]+[4,-5,2] lies on the planes 3x+2y-z = 10 and 7x+4y-4z=19.

A:

Q: X Edit 10. Rectangle GHU wilth verlices G(2.-1), H7.-1), 17.-4), and

A: Graph plotting

Q: a(x,y) Let G(u, v) = (5u + 2v, 5u+9v) be a map from the uv-plane to the xy-plane. Calculate Jac(G) =…

A: Given that be a map from the -plane to the -plane.The objective is to calculate .

Q: Let R denote the rectangle with corners (−1, −2), (4, −2), (4,1), and (-1,1), and let P denote the…

A:

Q: Let 5x + 3y + 10% = 0 be the equation of the 3 plane in R³ spanned by (1, a, 0) and (1,0, b). Find…

A:

Q: The vertices of AJKL are J(-3, 4), K(3, 0), and L(-5, -4). The equation of the median JLis y = 0.…

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: Find the orthogonal projection of y = 8. 4 on W (1)-8} Span

A: The given problem is to find the orthogonal projection of y on the W is span of 2 vectors.

Q: Let line l : x=y/2=z/3 and point P(1,0,1). Find an equation of the plane (in point-normal form)…

A: Solution of given question is written in below steps.

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: A point moves so that sum of the squares of its distances from the vertices of a triangle is always…

A:

Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

Q: Let L, be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

A:

Q: 2) Consider a set of points {(-2,-18), (-1, -7), (0, -2), (1, -3), (2, -10)}. a) The least squares…

A:

Q: Let T : R^2 → R^3 be a linear map. What are the possibilities for the pair of numbers (dim Null…

A:

Q: 4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the…

A:

Q: Consider the integer points on the xy-plane. How many paths are there from (0,0) to (4,-2)? Only…

A: Consider the integer points on the XY plane. To find paths from (0,0) to (4,-2). Here only down and…

Q: Calculate the distance from point B=(−1,3,−1) to the plane that passes through point A=(3,2,−1) and…

A: