Find all the eigenvalues and the corresponding eigenvectors of the matrix A = = 6 2 -2 2-2 5 O 7

Q: Define a binary relation =3 on Z by x=3 y if x - y is divisible by 3. 1. Prove that 3 is an…

A: There is a relation on Z such that x is related to y if (x - y) is divisible by 3. Our aim is to…

Q: Set up a double integral to represent the area of region D, the region outside the circle r=3sin and…

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Q: Let C be the ellipse given by ² + y² = 1. () Find a polar equation for C. () Find a parametrization…

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Q: Question 4 (Unit 5) 21 marks (a) Find the eigenvalues and eigenvectors of the matrix A = H - (b)…

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Q: Find the matrix A of the quadratic form associated with the equation. 6x² - 4xy + 6y² + 16z² - 23 =…

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Q: Problem 2: Let A 11 [ -2 0 0 -1 - 1 002 2 (1) Find the eigenvalues and eigenvectors of A; (2) Find…

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Q: Let → F = . Use Stokes' Theorem to evaluate SSS curl → F.d S, where S is the hemisphere x^2 + y^2 +…

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Q: - [a C b If A = where a, b, c and d are real numbers, then prove that A²-(a + d)A + (ad-bc) I=O.…

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Q: True or false questions. (Hit the right "x") 11. a/ /bax b=0. 12. Let z=f(x, y), then 66 ✓" ,hit the…

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Use the simplex method to solve. Minimize subject to: The minimum is w = when y₁ = y (Simplify your…

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Q: Suppose that sin(a) = 4/6 and cos(b) =1/6 define in the first quadrant, determine sin(a-b). (round…

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Q: By showing that any sequence in A ∪ L has the same limit as some sequence in A, prove that…

A: To prove that A is a subset of A ∪ L, we need to show that every element of A is also an element of…

Q: H be the set of all points (x, y) in ℝ2 such that x2 + xy 3y2 = 3. Show that H is a closed subset of…

A: Answer given below.

Q: Please do fast

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Q: Dashing Dan is driving south on Sunset Boulevard, where the speed limit is 40 miles per hour. He is…

A: A police officer is sitting 33 feet due east of the intersection with her radar tuned to Dan's car.…

Q: 10 Show that (pVg) ^ (p Vr) → (q Vr) is a tautology. (construct the truth table)

A: The given statement is (p∨q)∧(¬∨r)→(q∨r) To check if it is a tautology draw the truth table

Q: Find a single matrix for the transformation that is equivalent to doing the following four…

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Q: In order to sketch the graph of f'(x), we must have a formula for f(x). O True O False

A: False.   See Explanation in step-2.

Q: -2 -3 8 8 Let A ₁ 1₁ - ( -3² -1²³), and 4₂ - ( 2³₁ - 2 ) be = = 5 -1 -5 two matrices in M. 22 Choose…

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Q: In bucolic farm there a contagion spreading among 500 happy cows, some with spots others with- out.…

A: Given Data: Total number of spotted and non-spotted cows =500 Let S=S(t) be the number of spotted…

Q: We have to determine whether the following series is absolutely convergent, conditionally convergent…

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Q: f(x^2+y^2  ,  y^2+z^2  ,  u^2+xy)=0  This is a solution of PDE. I need a suitable  Partial…

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Q: Let λ ER and consider the matrix J = 1 0 X 0 0 00 1 0 0 λ 1 0 0 X € M4. (a) Show that A is the only…

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Q: Write the form of a particular solution to y(³) + y" C₁ out determining the coefficients, given that…

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Q: 4. Find the slope of f(x) = hundredth. -3x-1 at (2,-1.65). Use a graphing utility and round to the…

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Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

A: We have to determine whether the following series is absolutely convergent, conditionally convergent…

Q: Find the flux of the field F(x,y,z)=z¹ i+xj- 6z k outward through the surface cut from the parabolic…

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Q: 6. SET UP the double integral which gives the volume of the solid in the first octant enclosed by…

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Q: Evaluate the Laplace transform of f(1) = { ; 0≤t <% cost ; t≥% 0

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Q: A. Find the tangent plane at x = 1/3, y = 2/3 of the surface z = ²+ln(x+y). B. Estimate z(.25, .60)…

A: x=13, y=23 Equation of surface: z=yx+lnx+y

Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

A: A series is a sequence whose nth term can be expressed in terms of 'n'.  A series is convergent if…

Q: Find the area of the region enclosed by y = 0.75 and = 5.5 - y². -4 -3 -2 -1 1 1 -2 -3 1 2 3 4 n Q…

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Q: If S= √√√3-1 2√2 √√3+1] 2√2 √√√3-1 2√2 A √√3+1 2√2 P = S (adj.A) ST, then find matrix ST p¹0 S. and

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Q: Problem 1: Diagonalize A and compute SAS-¹ to prove this formula for Ak: A 1 - [54] has Ak A² = [*…

A: Answer given below.

Q: Use L'Hospital's Rule to evaluate the following limits. ex-1 a) lim (x²-x³)e²x b) lim X118 x−0 tanx…

A: Given, a) limx→∞ (x2-x3)e2x b) limx→0 ex-1tanx c) limx→(π2)- (tanx)cosx We have to evaluate the…

Q: Please examine these two right triangles. 5.2 B Triangle A C 15 A A Triangle B 32° 10 C B If you…

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Q: Using the fact that A/B = An Be, show that in a metric space, bdy(A) = bdy (Aº)

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Q: EXTRA CREDIT Find the total area between the graph of f(x) = x² – 11x + 24 and the x-axis on the…

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Q: Writing In Exercises 7-14, explain why S is not a basis for R². 7. S = {(1, 2), (1, 0), (0, 1)} 8. S…

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Q: 2. Show that 27 | (5²² – 4).

A: We shall make use of Eulers theorem to solve this problem. The details are furnished in step 2.

Q: Match the following 10 functions into 5 pairs. If f(n) is paired with g(n) then f(n) = 0(g(n)), log₂…

A: As per the question we are given 10 different functions from which we have to find the 5 pairs in…

Q: Question 3 Consider the differential equation x²y" - 3xy' + 3y = 2x³ - 3x². (a) Verify that y₁ = x…

A: x2y''-3xy'+3y=2x3-3x2

Q: The set of polynomials {3t²-3t+5, mt+6t²+10} is a linearly dependent set in P, if 2 m=6 Select one:…

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Q: If an+1 = 2an + 3 and a0 = 1, then a7 =

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Q: Asap plz

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Q: Problem: A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of…

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Q: (D² − 1)y=e*(x² + 1)

A: THE HOMOGENOUS EQUATION IS , D2-1y=0 SO, THE AUXILLARY EQUATION IS, D2-1=0⇒D=1,-1 THE HOMOGENOUS…

Q: Find a single matrix for the transformation that is equivalent to doing the following four…

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Q: Draw the graph and find the Fourier transform of f(t)=e-at, a>0.

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Q: 4.6.11. Prove the following identities. n+2 2n (a) n i=1 =2- (for n ≥ 1).

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