A plane passes through the points A, B and C with coordinates (9,1, –4), (13, —4, 7) and (4, 2, −5) respectively. Find the vector → → product AB x AC.

Q: Let A; be elements of T for i E I. Show that Uiel A¡ E T.

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Q: → (a) Write down the vector AB joining the points A and B and with coordinates (1,3,-6) and (-9,…

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A: They form a basis for R3. Explanation is as follows

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A: Given that ∑s=231s+2∑s=231s+2

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Q: 59 Find the reference angle for the angle

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Q: Suppose that 2,..., are distinct eigenvalues of matrix A with corresponding eigenvectors…

A: Given That : suppose λ1,λ2,λ3,...,λn are the distinct eigenvalues of the matrix A with corresponding…

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Q: 1. (a) Find a direct formula for the n-th term of the sequence (tn) defined recursively by t₁ = -1,…

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Q: Sketch the second order spline that fits the end points PO (0,0), P2(9,4) and tangents intersection…

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Q: Given the following non-linear model Min x² + y² + 2x²y + 2xy + 2x²y²-8x-6y-14zy subject to 2² + y²…

A: given model Min x2+y2+2x2y+2xy2+2x2y2-8x-6y-14xy subject to  x2+y2≤5 (1) formulate the first two KKT…

Q: 1. Karen is a hobby farmer from near Toowoomba in Southern Queens- land. She sells the lettuce she…

A: As per company guidelines we are allowed to solve maximum three sub-parts so i am solving first…

Q: ΤΗ ΜΑΤΗ ΜΑΤΗ ΜΑΤΗ ΜΑΤΗ ΜΑΤΗ ΜΑΤΗ ΜΑΤΗ ΜΑΤΗ ΜΑΤΗ ΜΑΤ hich one is correct and which one is wrong?…

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Q: Given the ODE: -(t-1) cos(y). y(0) -3 at Estimate y(1) using midpoint method, h = 0.5. Present your…

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Q: Given X = {1,2,3,4,5,6). Determine the T() of the following 3. E = {{1}} 4. E= {{1}, {2}, {3}, {4},…

A: Tau(Sigma) denotes the topology generated by the set 'Sigma'. So, (i) the null set phi and whole set…

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Q: the following statement. 'If yes, explain why. If no, provide a counterexample. For every real…

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Q: f: X→ Y and g: Y→V be bijective functions. Show the following: ) gof: X→V is injective. ) gof: X→ V…

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Q: show that empty set, X is an element of S intersection T in topology

A: Here We have to show that empty set must be in S∩T where S and T are topology on set X.

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Q: Let X = {a,b,c} prove that topological space on the set X T = {X. Ø, {b}, {a,b}} be a

A: Let X={a,b,c} be a set. To show that T={X,ϕ,{b},{a,b}} be a topological space on the set X.

Q: The rules of mathematical logic specify methods of reasoning mathematical statements. These rules…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: 1. Let T and S be topologies in X. Show that SnT is also a topology in X.

A: 1.

Q: Suppose that the set A={X₁, X2..., Xn}, X₁ ER" spans the entire space R", i.e. for any arbitrary…

A: Given: The set A=x1,x2,...,xn, xi∈ℝn spans the entire space ℝn, i.e. for any arbitrary n-vector…

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Q: Consider the function defined by f(x) = -(x + 1)² +5 if x 4 Graph the function. Is the function…

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Q: Question 1. 1. Find the limits of the following sequences as n → ∞ if they exist (Note: n N - {0}):…

A: Disclaimer: Since you have asked to solve only Q2, therefore, only this question is solved. Please…

Q: sixt S 18 What is the missing number? 30 1 S →XIS

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Q: Question No. 5) Show that a partition of a set S determined equivalence Relation on set S. (

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Q: find du u = 0, v = 1 and dz of the function (z = f(x,y) = x² + y2), where x = ue" and y = ve" at dv

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Q: Prove that the trivial G is faithful if and only if G = {1G} representation of a nite group

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Q: Explain: why it is =show_steps, please explain each part : (~P VQ) ^ (~PVR) =~PV QAR

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Q: The following data were obtained for a sample of 10 men from a height and Σ (x₁ - x)² = 120, Ey? =…

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Q: Q: Consider the set of francti of the complex plane with where how S a Ta, b; c, d (z) = az+b Cz + d…

A: consider the set of function linear transformations of the complex plane with ∞ adjoined.…

Q: Perform two steps of the Conjugate Gradient method for finding an approximate solution to the system…

A: Given : A=42-222-3-2-314     ,  b=1054            , x0=000 To Find : Approximate solution of the…

Q: Question 7: Use De Moivre's Theorem to (7.4) express cos³0 sin* in terms of multiple angles.

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Q: 3:7:4=27:_:_

A: 3:7:4=27:_:_ We need to find the missing values in the ratio.

Q: 4. Let W be a subspace of a vector space V. We define a relation: V₁ V₂ if V₁ V₂ € W. ~ 4a. Show…

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Q: i) The temperature in a bar of length L is described by the heat equation ди Ət Q202 əx² ди əx = for…

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Q: Consider the set R. Prove: (i) VxER, x 0 = 0;

A: Given x belongs to R(real number) If x=1 Then 1.0=0 If x=2 Then 2.0=0 Similarly  3.0=0 4.0=0 and so…

Q: Determine whether ⊂, ⊆, both, or neither can be placed in the blank to make the following true.…

A: Let A={bruschetta, pig's feet, cream, almond paste, rose water} B={pig's feet, rose water,…

Q: Find two linearly independent solutions of 2x²y" - xy +(-3x+1)y=0, x > 0 of the form y₁ =…

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