Let A E L(U, W), BE L(V,U) a (a) Show that (AB) = Bt At.

Q: = f(x,y) = e²+y. For a unit vector u in R?, it is fü(0, 0) = 1. Let z true that

A:

Q: Let ʼn be a positive integer and let u(x, y) = (x² + y²) Show that where C' is a constant depending…

A: ux,y=x2+y2n∂2∂x2+∂2∂y2ux,y=Cx2+y2ux,y

Q: Let x = s e and y =t es. Compute the Jacobian

A: Given: x=set and y=tes.

Q: Find an upper triangular U (not diagonal) with U2 = I which gives U = u- 1.

A: Given, U2=I

Q: Let T ∼ Γ(4, 0.5). a) Find μT. b) Find σT. c) Find P(T ≤ 1). d) Find P(T ≥ 4).

A: a) Mean: Thus, the mean µT is 8.

Q: 1. Let f(x,y,z) = 2.x* +8yz' +8 . Find f(0,5,1). A) 48 B) 128 C) 48 D) 9 E) 22

A: Given f(x,y,z)=2x3+8yz3+8f(0,5,1)=2(0)3+8(5)(1)3+8

Q: 1. Compute d e (z²) (sin(t) + e*)v= dr

A:

Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: If A is an arbitrary vector and R and S are arbitrary dyads, verify that: (a) (I x A) R = A x R. (c)…

A: As per our company guidelines, we are supposed to answer only the first three sub-parts of the…

Q: Suppose that 7 (t) is a vector-valued function. Prove that d (7 · (7'x 7")) = : (7' x 7") dt

A:

Q: Suppose V is a vector space and S, T = L(V, V) are such that Range Scker T=null T. Prove that (ST)²…

A:

Q: (-1)" 10. n A) 0 В) -1 C) 1 D) 2 E) Divergent

A: we have to solve the following

Q: Prove the following statements: d (a) [u(t) · v(t)] = u'(t) · v(t) + u(t) · v'(t). dt

A:

Q: 1. The General Social Survey asked a sample of adults how many siblings (brothers and sisters) they…

A: Since you have posted a question with multiple with sub-parts, we will solve first 3 sub-parts for…

Q: Find rsint V1+ u+du) dt. dx2 Jo

A: We have to use the formula  Here  We write the second derivative as two derivatives and use f(t)…