Matrix System x11(t) x12 (t) X22(t) X1(t) = and X2 (t) = X21(t)

Q: are orthogonal on einmx/L, n = 0, ±1, ±2,... [-L, L] with norm equal to √2L.

A:

Q: Form 2 of the chain rule. Do the following problems: A. Let z = u² + v²; u = 2x + 7, v = 3x + y.…

A: To apply chain rule for this problem, we first need to identify the composite functions involved.…

Q: Prove that •1 to(xt) 1-1² dt = Sinx x

A:

Q: 3. Let f : R" →R be differentiable and fix ro € R". Assume Vf(ro) 0, where Vf(ro) is the gradient…

A: We will use the Cauchy-Schwarz inequality for vector dot product in order to prove the given…

Q: Suppose f(x, y) = xy + 4. Compute the following values: f(x + 4y, x – 4y)= - f(xy, 6x²y³)=

A: We can find the given function .

Q: Find the maxima and minima the function f(x, y, z) = xy²z³ under the condi- tions x + y + z = 6, x >…

A: The given function Let

Q: 5. Find the linear appoximation for the funciton f(x, y) = (ro, Yo) = (3,0). x-y xy+1 at the point

A:

Q: Which of the following is the orthogonal trajectories of the family of cissoids y² = ? a- y² = C(x +…

A:

Q: 2. Prove: a. [(x)b~ XE]~ = (x)b XA b. Эх (~p(x) A ~q(x)) = ~[Vx(p(x) V q(x))] 3 Dariva

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Q: Use the Wronskian and any needed theorems to show that f1 = sin x + 2x2 and f2 = e3x are linearly…

A:

Q: The following is the acceleration function for a particle moving in. a straight line: a(t) = 212 -…

A:

Q: directional derivativ e this information to

A: Given as, f1,2=3, i+j=0.7

Q: Let r(t) = ⟨t, t, t⟩. Compute r'(t) and interpret the result.

A: rt=t, t, t

Q: 4: Which of the following functions has gradient vector [4x₁x₂ 2x² 3x²]¹? A: f (X) = 2x{+2x3+x3x3 B:…

A:

Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

A:

Q: Let f(x, y) = x²y. Compute and simplify each of the following: (a) f(x + h, y) – f(x, y), and (b)…

A:

Q: Suppose F (x, y) = (2xe-", 2y – a²e="} (a) Find a scalar function f (x, y) such that F = Vf (b) Use…

A:

Q: Find the functionr that satisfies the following conditions. r'(t) = (1,4t ,5t4); r(1) = (7, – 6, –…

A: Given that

Q: The gradient vector of the function f defined by f(x,y)= In(1+7x² +5y²) is equal to Select one: O…

A:

Q: 10. Given R = x7 + y3+ zR, and r = |R show that (a) V x (7 x R) =7 + 7R, (b) (A x V) × R = -27, (c)…

A: Given: be any constant vector.

Q: 4) Find the Hermitian form [18] [2] X = H= XTAX where

A:

Q: Compute f, for f(x,y)=xln(xy). %3D

A: We can find the answers as below.

Q: Let S={(x,y)∈N×N|(2−x)(2−y)<2(4−x−y)}.Prove that S=TS=T, where T={(1,1),(1,2),(2,1),(1,3),(3,1)}

A:

Q: 2.) Are the following functions vector-valued or scalar-valued? a) f(u,v, w) = Cu²v, we, sv) b.j…

A: Answer given below.

Q: Let f(x,y,z) = x² e Vy*+ Compute f(3, - 5,3) and f(5,8, - 6).

A: Given that     f(x,y,z) = x2 e√(y^2+z^2)

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.