1. State and prove the Lagrange's identity.

Q: Give an example of the inner product in M3x3. Determine the length of the identity matrix Learning…

A: Inner product of the matrix

Q: ди 2х + ди วง =0, 4 (0,y) = зегу u

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Q: Prove or disprove any four of the following 2. Any field is a division ring.

A: We are asking whether ' Any field is a division ring ' or not .

Q: 3.x+y+z=4 - x=y+z=-2 2x -y + 2z=2

A:

Q: Q5) Solve the partial differential equation V²u(x,y)=x with the condit u(x,0)=0 , u(x,10)=0, u…

A: Using centered dufference formula for second order derivative.

Q: Let v1 = (1,2,1), v2 = (2,9,0), v3 = (3,3,4) . Show first that S= {v1, v2, v3} is a basis for ℝ^3.…

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Q: Let A be a nonempty subset of a bounded set B. Why does inf A and sup A exist? Show that (a) inf B ≤…

A: Use the following definitions, to prove the result. A set S is said to be bounded above if for…

Q: 6 4 A = 5 -5 4 -3 1 Find the images of u = = -7 41 -2 and 7 = a [B] с b under T.

A: Here, we use given linear transformation.

Q: Se¹0√1-e²0x dx 8.

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Q: Consider the physical quantities s, t, u, v and w. We would like to work with these quantities using…

A:

Q: Let f(x)= e2 sin 1. Use the local linear approximation of f at x = 0 to approximate e² sin(0.01). 2.…

A: Given function is f(x)=e2sin(x)     (1) Solution 1: We have to approximate e2sin(0.01) using local…

Q: 9. The inverse of an element a of Z under the operation * defined as a*b = a + b - 1 is A. a -2 C.…

A: Solution :  Options (B) is correct

Q: using Laplace transforms y"-2y' +10y = 0, y(0) = -3, y'(0) = 0

A: Solution :

Q: 2. Which of the following operations is associative on Z? A. a*b = a b C. a*b = a B. a*b = max (a,…

A: Solution :  Options (c) is correct

Q: Incidence Table 1 E4 E5 E6 E7 E8 A 1 1 0 0 0 0 0 B -1 0 1 0 1 0 0 C 0 -1 0 0 1 0 0 0 D 0 0 1 -1 0 1…

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Q: II. Evaluate the following integrals_ 9x - 5 4. J d.x 9x² 18x + 13

A: We need to find the value of ∫9x−59x2−18x+13dx…

Q: Use Dijkstra's algorithm to find the shortest path between nodes 1 and 7 in the following directed…

A: Given: A directed graph, To find: Shortest path using Dijkstra's algorithm.

Q: Let A ∈ (R) be given If A is nonsingular, prove that adj(A) is nonsingular and adj(A)^-1 = (A^-1)

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Q: 1. Let n = pq, where p and q are distinct odd primes. Define X(n)= (p-1)(q-1) gcd(p-1,q-1)* Suppose…

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Q: ADVANCED MATH (Round off the answers in the nearest ten thousands,  Evaluate J by means fo…

A: The trapezoidal rule uses the formula:∫abydx=h2(y0+2(y1+y2+y3+...+yn-1)+yn), where h=b-aN and N is…

Q: Prove the following result using the definition of subspace: Let (V,+,.) be a vector space over…

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Q: In tracking the propagation of a disease, a population can be divided into 3 groups: the portion…

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Q: 2. lim (x - Inx)* x →0+

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Q: ADVANCED MATH (Round off the answers in the nearest ten thousands,) Evaluate J by means fo…

A: It is a Numerical Analysis problem. Let us evaluate J using Trapezoidal Rule and also describe the…

Q: Write the equation y = 2(x+5)(x-4) in standard form. Determine the factored form of the trinomial…

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Q: 5. Use Cartesian coordinates to evaluate 구 y dv where D is the tetrahedron in the first octant…

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Q: (a) the domain of f (b) the range of f (c) the zero(s) of f (d) f(-1) (e) the intervals on which f…

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Q: a) Find, in terms of a, the equations of the lines tangent to these curves ) Find, in terms of a,…

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: Determine the truth value of the following statement. True or false the truth of the statement…

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Q: 0 -6 0 48:9 A = 0 0 -1 -8 0 0 3 Define the linear transformation T: R³ → R³ by T(x) = A. Find the…

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Q: f(x) X- COS(X) 1 + x 2 By using newton rafson find the solve.de ToL = 0.0005 1 X₂=1

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: Determine the truth value of the following statement. True or false the truth of the statement…

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Q: VII. Given a region R enclosed by the curves y = 1 + sin (7) 4 as shown below. Y (2,4) (2, 2) (-2,0)…

A: Given a region R enclosed by the curve y=1+sinπx4, y=4-x-224, x=2

Q: Consider the linear programming problem: Maximize/minimize z = -3x - y subject to: -10x + 5y ≤ 22…

A: We now find the x-coordinate of the corner point of the feasible region at which z=-3x-y maximize or…

Q: 14. Consider the group (A, *) where * is defined by the table below A B C D ABA D с BA B C D C D C A…

A: Let us solve the  Group problem related to composition table in the next step.

Q: condition o

A: It is basic business sincerity to be fully aware of all aspects of a product when looking to buy or…

Q: III. Consider the region R below bounded by the curves C₁ : x – 4y = 4, C₂ : y = √x – 1, and C3 : x…

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Q: 6. List 5 similarities and 1 difference between the graphs of y = sinx and y = cosx. Similarities…

A: We have to Write Five similarities and one difference between the graphs of the functions y =  sinx…

Q: Prove the following by using induction: 1(1!) + 2(2!) + 3(3!) +...... + n(n!) = (n + 1)! - 1, for n…

A: We have to prove the following by using induction…

Q: 5 A house was worth $675 000 in 2008. It was predicted to increase in value by 3.5% each year.…

A: here value of the house increases 3.5% each year, this increase in cumulative. so to find the value…

Q: 14.Consider the group (A, *) where * is defined by the table below * A B C D AB A D с BA B C DC D C…

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Q: Use separation of variables to find a product solution to the following: d²u du -u, k>0 dr -U= dr² k

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Q: 4. Let f(x) = √√2 cosx - x (a) Determine the absolute extrema of the function f on the interval…

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Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

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Q: -2x² Find the absolute extremum values of f(x) = xez 3 (Note: e 2≈ 0.22) on the interval [0, 1].

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Q: Consider the region R below bounded by the curves C₁ x - 4y = 4, C₂ : y =√x - 1, and C: x + 2y = 4.…

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Q: (13* - 11 + 13" - 31) da

A: The absolute value function: y can be defined as: y=-y,y<0yy≥0. It is known that ∫axdx=1ln aax+C.

Q: 2) Draw shear force and bending moment diagrams of the beam and find the maximum values of the shear…

A: Solution :

Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

A:

Q: of the following is a subgroup of (R+, *) where a*b = (ab)/2? A. (Q, *) B. (Z.*) C. (Q+, *) D. (Q-,…

A: Given group G = ( R+ , *)  where ,                       a*b = ab2 (.)  Group :  Let G be a non -…