et A = Y a 1 1 -1 2 -1 1 1 2 3 5 05 2 3 5 where a is a scalar. Show that det(A) is independent of a.

Q: x-y, z + y + 3,z²) and the net is decribed by the equation y = 1- x² - z on

A:

Q: 2. For the vector field V = (7x³ + 2y2²)i + (4x²z - 7y²+3)j + (4y³ +2² -32²) k find the divergence…

A:

Q: 5) Show that the u = f(x + ct) + F (x – ct) satisfies the wave equation in one-dimensional space.

A: Given: u=fx+ct+fx-ct       1 Differentiating wrt x ux=f'x+ct+f'x-ct Again differentiating wrt x…

Q: 1) The domain of the vector position r(t) = 1+2 i+ sintj+ In(9- t²) k

A: We are entitled to solve only 1 question at a time so, I am providing you the solution of the first…

Q: Express the following vector function in a component form. r(t)=t°j+(cos 2t)k

A: The vector function is given as , rt=t3j^+cos2tk^ express in component form.

Q: If F(x,y,z)=1i+2j+3k, then O1. P=1 Q=2 and R=3 are vectors of F. O II, P=1 Q=2 and R=3 are gradient…

A:

Q: Q2.4 that satisfies the following determine a vector function conditions outlined below: r"(t) = 3…

A: We are given that        r"(t) = 3cos(5t) i + 8sin(6t) j + t6 k   So, integrating both sides, we get…

Q: (c) If and are smooth scalar fields, show that V x (6V) = Vox V

A:

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: 7. Let C[-7,7] be the vector space of continuous function over [-n, 1] with an inner product 1 (5,9)…

A: C-π,π is a vector space of continuous function, with inner product <f,g>=1π∫-ππfxgxdx show…

Q: Consider the vector space of solutions W to the differential equation y(3) + 7y(2) + 14y/ + 8y = 0…

A:

Q: Consider the model (1–0.4B)Vx, = z₂, where B is a Backshift operator and z, ~ WN(0,4). a) Write down…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 4 sub-parts under part…

Q: Suppose we have a vector field Ē(r, y, z) defined by Ẻ = –Vø. Prove or disprove the following…

A:

Q: Which vector field would generate this graph? 0( - y, – a) O (y, z) O (x, – y) 0( - 1, y)

A: We check the given vector field one by one. First one is fx,y=-y,-x Now, for point 1,1 we see that…

Q: where r is the position vector 6. Show that A) - da = | (Ax (Vf)) · da + fA- dl 7. Evaluate the…

A:

Q: 1. Obtain the directional derivative of: a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction…

A: Step 1:

Q: A scalar field is given by f = x2/3 + y2/3, where x and y are the Cartesian coordinates. The…

A:

Q: 4. Given the vector equations below, find the value of the scalar k, such that a = kb. [T4] * = + *…

A: To find the value of a scalar k by the given vector x→=35y→+25z→

Q: [#1] Exercise 7.46. Prove that if y = y' then y = ky' for some scalar k.

A: Given that γ≡γ' The y can be written as,  γ≡r mod n The y' can be written as, γ'≡ r mod n

Q: (a) P, Q and R are differentiable vector functions in R³ and is a scalar u. Show that dQ du [PX…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let xbe inner Product and ||x1|=|ly|| = 1 x+y Lix.y ? why?

A: Given that X is an real inner product space. x ,y be two unit vector from X then need to show that…

Q: 3. Use the Wronskian to determine whether the functions fi = e*,f2 sinx and f3 = x are linearly…

A: To find- Use the Wronskain to determine the functions f1 = ex, f2 = sinx and f3 = x3 are linearly…

Q: dr = wa x b dt r X

A: