. Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly dependent set in R4? . Express V1 in number 1 as linear combination of V2 and V3

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A: Solution : Conditional probability: probability of A given that B already happened. P(AB)=P(A∩B)P(B)…

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Q: 5. Consider the following function: f(t)= Find the Laplace transform of this function. Lis odd -1 is…

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Q: 1. Determine the absolute extrema of f(x) = (cos x − 1) sinx on [0, π], if they exist, and identify…

A: As per our policy, we are allowed to attempt only first question. Kindly post remaining question…

Q: QUESTION 3 A manager wishes to simulate 10 days of operation of an inventory system. The beginning…

A: Solution :-

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A: We can solve this using given information

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A:

Q: 10x + 2y — z = 27 -3x - 6y + 2z = -61.5 x + y + 5z = -21.5 L == Answer x = y = U = N ||

A:

Q: Find the area bounded by the curves y - x² = -3,x+y = 3 and y = 0.5x.

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Q: 23: Use finite difference method to solve Laplace equation in the Homain illustrated below. Ax = Ay…

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Q: Set up the integral which yields the arc length of the portion of C2 traced counterclockwise from B…

A: This is a question from the application of calculus.

Q: 5. Find all the solutions of the system below. 1 • (-) = -(+) a. y C 0 b. (+1) = c(-¹) y C -1 1 1 2…

A: 1211-11212xyz=000

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Q: 8x Show that the three functions: f₁(x) = ex-8, f₂(x) = e³x, f(x) = 4(2x-2) are linearly dependent.

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Q: Find the area bounded by the curves y - x² = -3,x+y = 3 and y = 0.5x.

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Q: Mrs. Cruz asked her 30 students who among their mother, father, or sibling will attend the quarterly…

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Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: 3. Solve the linear system using Gauss-Jordan method I 2x+y+z=2 y+z+w=2 x+y=z=0 x + 2z-w=1

A: augmented matrix of the given system 211020111211-100102-11

Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

A:

Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

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Q: Find the complete solution of ds dt = 8t³ √√s. =

A: Here we have given dsdt=8t3S ds=8t3sdt dss=8t3dt ∫dss=∫8t3dt ∫s-12ds=∫8t3dt s-12+1-12+1=8t3+13+1+c…

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A: Real valued function: A function whose domain and codomain are subsets of the set of real numbers ℝ…

Q: List the elements of each set where N= {1,2,3…} a.) A = {x∈ N | 3 < x < 9} b.) B = { x∈ N | x is…

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Q: a) Answer the following questions, in how many ways: i) Can we select 6 persons to sit together at…

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A: Variation parameter method

Q: Consider the series an +∞ and Etibn where cos(3) and bn 1 n³ n3 an =

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Q: 5. z = yex+x Iny xey-y lnx

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Q: Solve the following ODE in the range [0, 0.2] using h dy y(0) = 2, -t+y=0, dt² = 0.1 with explicit…

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A:

Q: 3. Evaluate Iffa a x dV, S is the tetrahedron bounded by the S planes x+y+3z = 6, x = 0, y = 0 and 2…

A: We have the that S is bounded by the planes : x+y+3z=6x=0y=0z=0 So, from x+y+3z=6 we get z=6-x-y3…

Q: x² A quadric surface is defined by the equation: + 3y² = 3 + z 3 1. Solve the equation of the traces…

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Q: Let M be a matrix a M-[b] = c d Matrix M is non-singular if and only if O ad + bc #0 O ad - bc #0

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Q: 3√2 √2 cos 2 2 Consider the polar curves C₁ : r = 4+² cos 0 and C₂ r = 2- as shown in the figure on…

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Q: 36. Sin(xy) + cos(yz) = 1. Compute z and az at P = (2, п/12,4). дх ду

A: Let us consider the given function z=f(x,y) The partial derivative of the function is obtained as…

Q: and m' be two R-modules. e set Hom, CM, Mm) is an group under pointwise of morphism

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Q: Consider S as a quadric with equation 4x² − (y − 3)² + 4z² = 4 1. Classify quadric type of S. 2.…

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Q: 3. Prove that: na” u[n] = az (a-z)2

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Q: Given a Euclidean space E there is an orthonormal basis t. this basis is a diagonal mat λ₁

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Q: E be a Euclidean space of dimension (E(1, f)) = dim(Ker (f- id)), then s minimal.

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Q: Lett: V→ V' be a linear transformation. Then (1) Ker (t) is a vector sub space of V, and (ii) im (1)…

A: The solution is given as

Q: 2. Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y² - 3x² and…

A: Using trigonometric substitution

Q: Given: planes II₁: 2x - 5y + z = -1 and II₂ : x + 5y + z = 5 intersecting on a line l (a) Compute…

A: Given: Planes π1:2x-5y+z=-1 and π2:x+5y+z=5 intersecting on a line l.

Q: 5. The von Bertalanffy equation is defined by the ODE W'(t) = aw (t)-BW (t) where is a constant…

A: The von Bertalanffy equation is defined by ODE as follows W'(T) = αW(t)2-βW(t)Let  y(t) = W1-λdWdt =…