If A is diagonalizable, show that A3 is also diagonalyable.

Q: 3x 2х, +3к3 =0 X2 +2*3 =3 - 2x1 +*2-2

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Q: Consider the following 6 equations: 5x - 4y + 2z+3v+w=47 1x1 - 3y - 3z 5u=-22 -3x-y 3u + v 4x + y 3v…

A: According to the given data, find the solution:

Q: Consider the subspace H of R* given by −2a + 2b + 4c -26 H -4a + 8b+8c -2a + 4c : a, b, c = R a.…

A: The given subspace H isreducing to  RREF fromApplying   this is the reduced row echelon form

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 2. Find one of the two roots of the equation x² - 4x +2=0 using…

A: We have to find the root of the equation in fixed point iteration we first fix a point from where we…

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Q: A vector v = (V₁, ..., Un) € R¹ is said to be strongly positive if v¿ > 0 for all i = 1, ..., n.…

A: Explanation:A vector is a quantity which describes the magnitude and also describes the movement of…

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Q: How do we prove the following by doing a direct proof? " Let a  ∈  Z. Prove that if 3|2a, then 3|a."

A: This question is done by the help of number theory concept.

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Q: For the transition matrix P = 0.1 0.9 0.3 0.7 solve the equation SP = S to find the stationary…

A: Explanation:The transition probabilities between states in a Markov chain are represented by the…

Q: 1. The equation f(x) = x² - x cos x has two roots in the interval [0, 1]. Determine how many…

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Q: Convert the polar equation to rectangular coordinates. k a+b sin r = ' where a, b and k are…

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Q: Solve the following differential equation. dy x=3y

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Q: e. Consider our original homogeneous equation: y" +2y' +5y = 0. Rewrite this as a system of first…

A: e. Consider our original homogeneous equation: y''+ 2 y'+ 5 y= 0. Rewrite this as a system of…

Q: 17. Let S = {1,2, 3, 4, 5). The vertex set of a graph G is the set of 2-element subsets of S. Two…

A: The Petersen graph is a well-known and interesting graph with 10 vertices and 15 edges. It is named…

Q: = Use the Maclaurin series for f (x) = 1 + 2x to determine the Maclaurin series of g (x) = ✓(1+2)…

A: Given…

Q: Determine the largest eigen value and the corresponding eigen vector of the matrix. (a) (b) [1 A = 1…

A: Given:It is given that,(a) (b) To Find:We have to determine the largest eigenvalue and the…

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A: Given: A toy's company has a factory that produces toy trucks and toy cars. The total number of toys…

Q: Solve the following initial value problem: (-xy + 2x + 2y - 4) dx + xy dy = 0, y(1) = - 1 OT/P

A: We have  initial value problem and we have to solve this problem using substitution method.

Q: Find the surface area of the part of the cone x² + y² = z² between the planes z = 3 and z = 8.…

A: We need to find the surface area of the part of cone  in between the plane  and

Q: 2. Suppose that z is implicitly defined to be a function of z and y by the equation e'z +2'y əz Use…

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Q: Solve the following differential equation. y + y +y=x²-2x

A: We have to solve the given differential equation.

Q: Suppose that W is a subspace of R" with an orthogonal basis {w₁,..., wp} and suppose that {V₁,...,…

A: In this question , we will check the given statements is true or false.

Q: 3. Find the integrating factor for the DE. *Then solve. dy dx - 2y = 3e²x

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Q: Let Find an orthonormal basis of the column space of A. 121 1 0 -27 2 -4 4 A 2-4 0

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Q: Problem 7: With the graph below: .Write out the adjacency matrix. • How many walks there are from…

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Q: 0

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Q: A(2, 4) and B(2,-2) are two points in a rectangular coordinate plane. A moving point P(x, y) lies on…

A: a)  Given that Co-ordinate of the point A is    and Co-ordinates of the point B is      Suppose that…

Q: Use now reductions to fine A-! A (1 2 4 -3 4

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Q: a) x4 - 20x2 + 64 = 0 x+4 b) 하는 -4 x+2

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Q: Find the polynomial of least degree that interpolates the data x 3 7 1 2 f(x) 10 146 2 1 in (a)…

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Q: A young pair of rabbits (one of each gender) is placed on an island. A pair of rabbits does not…

A: We have to find a recurrence relation for the number of pairs of rabbits on the island after…

Q: Solve the following differential equation. y"+y' - 2y = 0

A: Given:The given differential equation is .To Find:We have to solve the given differential equation.

Q: Compute the Jacobian at the indicated point. G(r, t) = (r sin (t), r — cos (t)), (r, t) = =(5,2)…

A: Jacobian of the function

Q: Exercise 1. Partial Parabolic Equations: Classify the following equation: 3 Ou Əy

A: Here for given partial differential equation we have to classify it.

Q: y'=(y-1)^2(y-2) plot phase line Identify equilibrium point and clasify stability

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Q: Use the Laplace transform to solve the following initial value problem. y' + 2y = eºt, y(0) = 2

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Q: can you do this one more time pls

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Q: Which of the following statements is (are) false if all vectors are in R"? O a)Not every orthogonal…

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Q: Study the continuity of functions when the weak topology is considered in the starting space, and…

A: As per the question, we are asked to study the continuity of certain linear transformations between…

Q: bc a b If def-4, find 2d+g 28+h 21+1 ghi a b c 2d+g 2e+h 21+i (Simplify your answer.) ghi

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Q: Let F = (, , 2). Calculate div (F) and curl (F). (Use symbolic notation and fractions where needed.)…

A: We have to calculate  and .

Q: Given that x² + y² + z² = 6 and (055) w w³ + z³ 5xy + 12. Find for x=1, y=0 and z=7. ( ($).

A: Given,                   and To find the value of for

Q: Let f be an integrable function on a measurable set E. Then, + ½ [ f(x)\dx f = 0 a.e. = 0

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Q: Q2. 600 people (250 less than or equal to 20 years old, and 350 greater than 20 years old) were…

A: Given: A survey was taken in which people (less than or equal to  year old, and  greater than  year…

Q: Let v = (r³ cos z, 4 - 3x²y cos z - 3yz² sinx, 2³ sin x) be the velocity field of a fluid. Compute…

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Q: Evaluate fff zdV, where E E is the region shown on the picture. It is a half of the ball of radius 1…

A: Given integral is where E is shown in given figure.We convert the given integral Cartesian to…

Q: Grade-point averages. Find the mean and median for the grouped data in the following table.…

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