thogonal projection of y onto u. ne distance d from y to the line through u and the origin.
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Q: 10. Given ủ [10,4] and i [12, – 13], find the projection of i on v. %3D %3D
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- Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.If V=R\power{3}, and W\index{1} is the xy plane and let W\index{2} is yz-plane: W\index{1}={(x,y,0):x,y∈R} W\index{2}={(0,y,z):y,z∈R} then V is not the direct sum of W\index{1} and W\index{2}.What is the 3 by 3 projection matrix I -nn Tonto the plane jx + jy + ½z = 0? In homogeneous coordinates add 0, 0, 0, 1 as an extra row and column in P.
- IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square 0<= x <= 1, 0<=y<=1, in the xy-planeIn isosceles triangle XYZ, XY = YZ = 10, and XZ = 16. Where C is the centroid of triangle XYZ, find the distance from C to side XZ of the triangle.Use Green’s theorem to evaluate ∮C(ye2xy−5y)dx+ (xe2xy−2x)dy, where Cis the counterclockwise oriented boundary curve of the square with vertices at(0,0), (0,1), (1,0), and (1.1).
- A vector y in Rn can also be viewed as an n × 1matrix Y = (y). Show that ||Y||2 = ||y||2: A parametric cubic curve passes through the points (0,1), (2.5), (3,5) (5,-3) which are parameterized at t=0.1, 0.3, 0.6 and 0.9 , respectively. Determine the geometric coefficient matrix and the slope of the curve when t-0.5.Determine the position of the y-centroid of the line from x = 1 to x = 5.
- Find the image of the annulus 1 < |z| < 2 under the transformation w = z/z −1 Please dont provide hand written solutioncompute and attach a photo of neat computations of: The area of the triangle on the plane x+y+z=1 which is the orthogonal projection of the triangle of vertices A=(2,1,1) B=(2,3,2) C=(-1,-1,0)
