Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the vectors (6,5) and (7,4). (Give your answer in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) T(u, v) = Calculate the double integral of e²x-yover P via change of variables. (Express numbers in exact form. Use symbolic notation and fractions where needed.) 1₂ ²²x e²x-y dA =

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: Find the scalar and vector projections of b onto a. a = 3i- j + 4k, b =j + (1/2)k compab = projab =…

A:

Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

A:

Q: Let l be a straight line that passes through the origin and is parallel to the vectors…

A:

Q: Compute the orthogonal projection of u onto v. Use the square root symbol '' where needed to give an…

A:

Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

A:

Q: Find a unit vector u that is normal to the level curve of f(x, y) = 5x²y through P = (x, y) = (5,-4)…

A: Solution:Given: ,            we have to find a unit vector  that is normal to the level curve of…

Q: Qs, find Thi domain of He function

A: Given the given function is fx=1-x. Domain→it is the set of input values at which the function is…

Q: Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

A:

Q: 4. a) b) Let x = 27 + 3j - k, y = i- j + 4k and Z = −3ỉ + ]. Express the vector x – ỷ – 3ž in terms…

A:

Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned by…

A: The linear map G maps  to the parallelogram in XY-plane.The parallelogram is spanned by the vectors…

Q: Find the cross and v= product uxv² where û =8i +25 - 2k (-3,-1,8)

A:

Q: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

A:

Q: - 16] [1] Determine whether the vector v =| 17 |is spanned by the vectors and | 2 or not. 18

A:

Q: Let a and b be vectors in R?. (a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain…

A: Given: a,b∈ℝ2 If a=a1,a2 and b=b1,b2 then areaa,b=a1b2-a2b1. To do: Express the area2b+5a,b-2a in…