Prove the following statements (a, g is multilinear and alternating (b) If V=F", W=F₁ and T=LA for some A Man (F), then 9 = (det A/. f

Q: If f is continuous for t > 0, the Laplace transform of ƒ is the function F defined by: F(s) := |…

A: The solution is given as

Q: 31. Let f(x) = [x²/3]. Find f(S) if a) S= (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: The given function is, fx=⌊x2/3⌋. To Find: f(S) for the following set S, (a) S=-2,-1,0,1,2,3 (b)…

Q: If 9 = {(1, y) |1 ≤ x ≤ 3,3 ≤ y ≤ 6}: D then: 11,3 dr dy

A:

Q: If f-(a, b) = 0 and fy(a, b) = 0, then Vf(a, b) = 0.

A: Given,           fxa,b=0   and   fya,b=0

Q: (2 3. Let A = G) and B = (; ). Compute and compare: %3D a. Det(A + B), det(A) + det(B). b. det(3A),3…

A: We have A=2-135 and B=1211 Part(a) Now if we have a matrix M=abcd, then, detM=abcd=ad-bc Therefore,…

Q: Determine fx when S(r , y) (x² + 2y)(y² – x) .

A: Given f(x,y)=x2+2yy2-x. The main objective is to determine fx.

Q: If p is T and q is F, then p V ~q is OT OF

A: p is T, q is F p∨~q ~q (not q) = T

Q: 1) slz) = 3 -3 A) Yes B) No

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Which of the following is the parent function for a) f(x) = x b) flx) = x c) fx) = Ix| d) flx) = Vx

A: Given function is y=23x2. We have to find the parent function of y=23x2. The parent function is…

Q: sst. Let f(x, y, z) = x³ yª + zª and x = s5, y = st³, and z = s

A:

Q: 2 Find (5a" + 4a*) da 1

A: We can find the integration value as below

Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

A:

Q: Given that y1(t) = t2 is a solution to the ODE: |3D - 2ty" – 5ty + 14y = 0, use the reduction of…

A: The differential equation is -2t2y''-5ty'+14y=0 and the solution is y1t=t2. Now, the second solution…

Q: 3. Let f : A → B. Then 1gf = f and f14 = f. Hint. You may use the fact that fg, for functions f, g,…

A: Let               f1 : X→Y , f2 : X→Y be two functions, then we say that the functions f1 and f2 are…

Q: 7. Compute gfg, the conjugate pair of f by g for f= (2, 3, 5, 4) and g = (1, 3, 2)(4, 5).

A:

Q: 2. Let f(x, y) = (2x – y,x – 2y); (x, y) E R × R, (R is set of real numbers.) a) Show that fis one…

A:

Q: 15) Find u x v for u = and v = .

A: Given vectors are, u = -7, 1, 12 = -7 i^ + j^ + 12 k^v = 2, 2, 3 = 2 i^ + 2 j^ + 2 k^

Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…