[10] (3) Consider the triangle, A ABC, in R³, given that the three vertices are = B с = GIVEN: S is the area of A ABC, FIND: S = (-1,2,0) (1,0,1) (0,1,-2)

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Q: Problem #9: Consider the following matrix. 40 A = 1 1 Find a matrix P that diagonalizes A. 1 +42060…

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Q: 1) Use the limit definition of derivative f'(a) = lim h→0 f(a+h)-f(a) h x to find the equation of…

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Q: Find the reference angle 'of 0 = −635°. Then, sketch in standard position and label 0'.

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Q: 3) Let A CR be non-empty and bounded. Show that sup{|x − y|| x, y = A} = sup A - inf A.

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A: The set of all 3×3 matrices of the form S=1abc1def1 We have to prove S is vector space or not.

Q: Use the formal definition of the limit to prove the statement rigorously.

A: To Prove: By formal definition of limits that limx→1x3=1.

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Q: Use Simpson’s Rule with n=6 to estimate the area underthe curve  y= ex/x from x =1 to x= 4.

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Q: Let f: RR be a Lebesgue measurable function. Prove hat there exists a Borel measurable function g: R…

A: Let f:ℝ→ℝ be a Lebesgue measurable function.

Q: Solve the following differential equation by using integrating factors. xy=9y-8x²

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A: From the graph, local maximum and local minimum points are explain in below images

Q: roblem 7: (4.10) Show that for any integer n ≥ 1, we have n Σk(k+1) = k=1 n(n + 1)(n+2) 3

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Q: T: R²R¹, 7(e₁)=(2, 1, 2, 1) and 7(e₂) = (-5,2,0,0). where e₁ = (1,0) and e₂ = (0, 1)

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A: Given: Fs=4s3, Gs=s-1s2-2s+5. To Do: Express L-1FsGs in terms of convolution.

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A: Use cosine formula for triangle to solve.

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Q: Given the d. subspace V={(x,y,z)=R³ | 2x+y-z=0} of the d. space (R³(R),+,-) and the vector…

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Q: A B C D E 1 2 3 4 0 F 5 G H 6 7 I 8 J K 9 10 L 11 M 12 U N O P Q R S T U V W X 13 14 15 16 17 18 19…

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Q: 2. Using the formal power series to prove the Vandermonde's identity n + b b ( #') = £ () (²x). k k…

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Q: 5. Let X be the space of reals with the topology T = {X, [0, 1], 0) (Example 2.1(b)), and let A =…

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Q: 9. If ƒ € R[a,b], show that få f(x)dx = limea 1 f f(x)dx = lime-a² f f(x)dx.

A: As we know on bounded interval Riemann integration is same as Lebesgue integration.

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Q: What is the next value in the following sequence? 5, 7, 11, 17, 25,... 33 35 37 39 41

A: The given sequence is ,  5 ,  7  , 11  ,  17 , 25 ,..........

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Q: Solve the given initial-value problem. y" + 4y = -5, y(л/8)= y(x) = - 1 y'(л/8)= 2

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Q: Solve this Homogeneous First-Order Diff. Equation: Hint: Partial fractions may be required for this…

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