The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. x² - 6x + 11 = 0 1 -3 A = and by the theorem you have A²-6A + 111₂ = 0 2 5 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 03 -1 A = -1 3 1 0 0 -1 STEP 1: Find and expand the characteristic equation.

Q: dy II. Find Do not simplify your answers. dx ㅠ 1. log;(√2æ² + y) + tan(xª — πª) = sin¯¹(x² − 1) + ½…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

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A: 1. True 2. True

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A: Here we have to find the arc length of the graph of r(t)=e√2ti+e-√2tj+2tk , 0<=t<=√2ln5.

Q: Consider S 1x². 2-9 x3 what is the integral form in terms of ? A / Scos² e de Ⓡ = sin²e de B C…

A: This question is related to Indefinite integration, we will solve it using given information.

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A: Given problem:-

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A: We can solve this as follows:

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Q: Find polar equation for the Cartesian equation 13y = 8x. a. theta = 1.02 c. theta = 0.55 d. r = 0.55…

A: Substitute x=rcosθ and y=rsinθ in 13y=8x. 13rsinθ=8rcosθ  13sinθ  =  8cosθ

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Q: Question 7 Let f(x) = 6x +11 f-¹(x) =

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A: A box with a square base and no top is to be made from a square piece of cardboard by cutting 6 in.…

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A: We can find the intercepts as below in the following steps.

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A: For domain, we will check for what values function is not defined.

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A: Formulas of limits which have been used are written in the solution

Q: 14. Evaluate the following √x-²sec (+)tan ³ ( =) « dx 2tan (²) [7tan² ( ² ) +11] +C 77 2tan…

A: To evaluate: I=∫x-2sec41xtan521xdx Substitute 1x=t⇒-1x2dx=dt⇒x-2=-dt So, I=∫sec4t  tan52t…

Q: 3. S 2 x²+a² x4 = _ (x² + a²) ³² 3a²x3 -dx = + c

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Q: [w (1-32)] 3w 11. lim w In 1 In W→∞

A: LetL=limw→∞ wln1-23wFor L hospital L=limw→∞ ln1-23w1wNow apply L hospital ruleL=limw→∞…

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Q: Let (A) = and B = . Find the angle between BO and A D O 【cos) 2/√(30(21)) O [cos] ^(-1) 2/√(30(21))…

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A: Here is the solution:

Q: d (h) (cot ¹(2)) = d (i)=(sec ¹(1))= = d (j) (csc-¹(2)) = dr 1 du 1+² dz 1 du I√²-1 dz 1 du I√²-1 dr

A: Given problem:-

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A: answer is in next step

Q: r₁(t) = cos(t)i + sin(t)j +5tk, r₂(t) = 4i + tk X d -=[r₁(t) · r₂(t)] 10 t - 9 sin(t) = dt d -[r₁(t)…

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