1-Find the cosine of the angle between A and B with respect to the standard inner product on M22 2 4 A = (-²₁₂3) B = (-3² ₂) 1 4 2 2-Let A, B E M .Determine whether if the function = tr(AB) defines an inner product on Mn?

Q: · y"(t)+5y'(t)+4y(t) = 0, y(0) = 1, y'(0) = 0

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Q: For which of the following matrices is [2 21 Ra [1] -41 [121 H an eigenvector with a nonzero…

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Q: Consider the function whose graph is the surface shown at the right. Which traces go with which…

A: From this picture, we can easily get the required traces

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Q: Find an orthogonal basis for the column spaces of the matrices in Exercises 9-12. 9. 3 [ - 1 3 ↓ I |…

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Q: Using the definition, determine the Laplace transform of the function. 3, 0≤t≤5 f(t)= t, 5<t≤00

A: Here the value of t ranges from 0 to infinity. We know f(t) is given we need to find F(s).

Q: Find the Laplace transform of the function f(t) = 3tª — sin(8t), t > 0. F(s) = S> 0

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Q: Wouldn't the values of r be something else for the integral? The shaded region starts at the circle…

A: The region shown in the figure.

Q: Let f(x) be a bounded, non-negative differentiable function on [0, ∞). Prove that the length of f(x)…

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Q: Use Green's Theorem to evaluate the line integral [(y-x) dx + (2x−y) dy for the given path. C:…

A: We  have  find  the  value  of  the  integral   where : boundary  of the  region lying inside the…

Q: Hello, hoe about #2

A: The given function is in branch We can find Laplace transform by defination .

Q: Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle…

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Q: For matrices in M,, (K) for a field K, which of the following is true (a) the product of two such…

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Q: Prove that for any two integers a and b with b>0, there exist unique integers q (the quotient) and r…

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Q: Suppose that g(x) has a critical number at c such that a 0 for x c. Determine the location of the…

A: g(x)  has a critical number at  c. Also note that  g'(x) &gt; 0  for x &lt; c,  that means  g(x) is…

Q: File Preview Assuming (AB)t = B¹A¹, det(AB) = det(A) det(B), and det (A¹) = det(A) complete any two…

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Q: Find at least the first four nonzero terms in a power series expansion about x = 0 for a general…

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Q: 3. Let the function f be defined by for - < x < π and satisfy f(x + 2π) = f(x). Recall that cosh x =…

A: 3. Let the function ƒ be defined byf(x) = cosh(x)for -  &lt; x &lt;  and satisfyf(x + 2) = f(x) .(a)…

Q: mh" +5h' +120h = mg h(0)=100 h'(o)=0

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Q: Min Z = 12X1 + 18X2 + 8X3  5X1 + 8X2 +9X2 >= 18  9X1 + 15X2 + 12X3 >= 36  10X1 + 15X2 + 12X3 >= 45…

A: Note:  In the first constrain  is given which is corrected to

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A: Find a unit vector in the direction of .

Q: Particular values of the marginal cost function of Kuddly Kites, a company that sells kites shaped…

A: Particular values of the marginal cost function of Kuddly Kites, a company that sells kites shaped…

Q: Exercise 10.4.6 Consider the linear transformation T: P3 → P3 given by T (p(x)) = p(x+1). Find…

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Q: 3. Show that Z10 is isomorphic to Z2 × Z5, but that Zg is not isomorphic to Z₂ × Z4.

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Q: The graph below is of a function g(x) with domain (-∞0, ∞). It consists of two lines and a…

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Q: urn contains six green balls and seven white balls. A sample of four balls is selected at random…

A: Probability calculations

Q: Do not use a calculator for this problem. Find the x-value where the relative maximum of y = e ² –…

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Q: In Problem 27 to 30, determine whether each statement is true or false. 27. 28. 29. 30. 7 1. 3 ≤9. 7…

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Q: Consider [0, 1] × [0, 1] with dictionary ordering. Find A, when A = {(x, y) : 0 < x < 1 and x + y =…

A: Given set            A = { (x, y) : 0&lt;x&lt;1  and  x+y=1 }We know that    where A'  is the…

Q: (g) Determine if h is surjective. Justify your answer.

A: The congruence ax=b (mod m) has solutions if and only if gcd(a,m) divides b. We shall be using this…

Q: An oil refinery is located on the north shore of a river at point A in the diagram below. They wish…

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Q: Problem 8. Let Rf be the set of all real numbers with finite complement topology. In this topology G…

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Q: Σ n=1 1 η3

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Q: Given below is a matrix A and an echelon form of A. Find bases for Col A and Nul A, and then state…

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Q: Let --->u =[2,-2,1] and --->v=[-3,5,-1] (a)  COMPUTE the distance between -->u and -->v . (b)…

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Q: Suppose that 11 female and 9 male applicants have been successfully screened for 5 positions. If the…

A: Suppose that 11 female and 9 male applicants have been successfully screened for 5 positions. If the…

Q: Find the volume using triple integrals of the surface in the first octant bounded by the coordinate…

A: In this question, we will find the volume in the first octant.

Q: Without​ consultation, each of three organizations announces a​ one-day convention to be held during…

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Q: Use Newton's method to find the two real solutions of the equation x4 - 3x³ - 3x²-3x+3=0. Compute…

A: Let, Find its derivativesx01234f(x)3-5-23-337Since the sign of the give function changes about and…

Q: [154] 10 (a) What is the largest eigenvalue, λ₁ of A? File Preview Let A = (b) Find a unit…

A: "Since you have posted a question with multiple sub-parts. We will provide the solution only to the…

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Q: 2. Assume that Σak <∞, prove that are converges uniformly on [-1,1].

A: We are given that ∑|ak|&lt;∞ , which means the series of absolute values of the coefficients…

Q: c) d² y dt² +2+y=4t, y(0) = 0, y'(0)=5 dt

A: We have to find the solution of the differential equation.

Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

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Q: Exercise 10.4.3 Suppose T: R³ R³ is a linear transformation such that →>> be another basis. 1…

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Q: File Preview A = 000 400 0000 06 020000 100 000 00 3000 50 00005 (a) Using any method, calculate the…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: b) Evaluate the integral by converting in polar coordinates [T 13 dy dr

A: (1) tan−1⁡(x)=cot−1⁡(1/x)(2) tan−1⁡(x)+cot−1⁡(x)=π/2 (3) 1/sin⁡(x)=csc⁡(x) .

Q: A company is attempting to estimate the average time that its workers spend on their breaks. Several…

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