Let V = M2x2 with inner product (A, B) = trace(B" A). LetA= B 4 0. -2. Then (A, B) and ||B|| All answers are numeric. • Previous

Q: for fa(a, y), let flg(2)) = (2² + y*)! %3D fa (2)%3D (2r)D %3D 2V + y2 3z (0) (i) (ii) 33z+y for…

A: We have to calculate the partial derivatives.

Q: Problem 3 Suppose that the functions y = 4 (constant), y2 = 2e2 and y3 = 3- e2 are solutions of a…

A: y1 = 4 y2 =  2e2x y3 = 3 - e2x

Q: A city is built on the banks of a river and some islands in the river. The map below shows the…

A: Given is a model showing bridges connecting various land masses. First a graph is to be drawn that…

Q: using f(x)=(3x)^2-5x-12, find f(-3)

A: Given    f(x) = (3x)^2 - 5x - 12 , then f(-3) = ?

Q: Let R be the region bounded by the curves y? = k(x- 1) and y = m(x- 2) as 2. shown in Figure 1. y? =…

A: We will use given relation between m and k and intersecting point to find values of m and k  . To…

Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

Q: 1. Find all the eigenvalues and eigenfunctions of the following Strum Liouville problem (3) 4(ey)' +…

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Q: Problem 5. Suppose v, w E V. Explain why there exists a unique r E V such that v+ 3.r = w.

A: Introduction: A vector space, also known as a linear space, is a collection of vectors that have…

Q: Problem 3: Consider a different matrix A: 1 A = Row vectors 1 1 -1 column vectors: a1 a2 аз (a) Find…

A: Given a matrix , A = 21011-1  . Also , given that the row vectors are r1→ = 210 and r2→ = 11-1 . The…

Q: Using Trapezoidal Rule to approximate the integral | sin(x)dx, n=1o What is T, ? Round off answer to…

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Q: Consider the vector field F = (x²y°, r’y²). O The vector field is not conservative O The vector…

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Q: Use mathematical induction to prove that 4 divides 5" – 1 for all n E N. -

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Q: The set of North-East lattice paths start from (0,0), end at (n-k, n+k), and they do not go below…

A: Given below clear explanation

Q: Let S be the subspace of P3(R) consisting of all polynomials p(r) such that p(0) = 0, and let T be…

A: The given vector space is ℙ3ℝ. The standard basis of the vector space is p1x=1, p2x=x, p3x=x2,…

Q: If [a11 a12 A = a21 and B = a22 [b11 b12 b21 b22] are arbitrary vectors in Rx2, then the mapping (A,…

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Q: Suppose that a small country with a population of 2,800,000 that consists of four states, A, B, C,…

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Q: Prove the following limit. ) f(x)=x²+2x+6 where lim, 3 f (x)= 21 >) lim x – x+1=-5 =) lim x³ = 8

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Q: 1. Mark as TRUE or FALSE. If they are true give an explanation, if they are false, give a coun-…

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Q: (a) Graph G, Graph G2 (b) Graph H, Graph H2 Figure 7-58 Graphs for Exercise 1. 2. Explain why graphs…

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Q: (e) 5. Compute the angle between the vectors [1, –1,0, 1] and [0, 1,0, 2]. 6. Compute the…

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Q: Let F be a field of characteristic 3. For a polynomial f e F(X], let f' be the derivative of f.…

A: Given: F is a field of characteristic 3. f' is the derivative of f. To do: Check which of the…

Q: Find the area of a triangle given below. Round your answer to 5 digits after the decimal point (if…

A: We have to find the area of the triangle ∆ABC whose sides are a=10 cm, b=5 cm, c=7 cm.

Q: 6. In the diagram shown, altitude AC is drawn from a right angle to BD in such a way that BC:DC =…

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Q: Solve the questions given below using the Fundamental Theorem of Calculus. r9(x) If f(x) = 1 rcos a…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 216 X(s) s4+5s3+15s2+45s+54

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Q: For which n listed below does there exist a field extension F ɔ Z/2 of degree n such that the…

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Q: Use the Jacobi method to find approximate solutions to x1 + 5æ2 – a3 = 5 21 +2 + 6r3 8 2x1 +2-x3 = 2…

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Q: Find Uncertainty for the equation below a*b3Vc R = vd

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Q: Part 4:  Hitting the ball into the parking lot   As Juan continued his hitting practice, one of the…

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Q: 2 (a) Find of the following functions: dx zxa+1cos y? = sin(yº + 22z) where A=2 C=6| 一

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Q: -ts) Consider the function e f (2) = (z – 2) (z – 2)? for |2 - 2| > 0. Find Laurent series expansion…

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Q: In 150 words explain the role of Mathematics in Accountancy field?

A: Blow given clear explanation

Q: Find the complete solution of the following partial differential equations. (i) p? + q² = 4x + 4y…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 4. Consider the following matrix A, where -2 4 -2 4 A = 2 -6 -3 1 -3 8 2 -3 Find bases for and…

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Q: 3-n (a) - 3n n=1

A: According to guidelines we solve one question.thanku

Q: Solve the problem. Maximize Q = x²y, where x and y are positive numbers, such that x + y = 540

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Q: 0 2 1 f). y" + 4y = g(x) ;y(0) = 3 and y'(0) = 0 where g(x) {-1

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Q: 16 e).y" + 2y = 48(t – 2n) ; y(0) = 3 and y'(0) = 0

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Q: A bond has a 14000 face value, an 8 year maturity and a 3.05 coupon. Find the total of the interest…

A: Face value = 14000 Coupon = 3.05% Thus interest rate = 3.05% = 0.0305

Q: If f(1) and g(1) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(-1)g(-1)+…

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Q: (a) Find the eigenvalues of A. (b) Find two eigenvectors v and w of A with respect of the two…

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Q: Problem 4 Consider the differential equation ay"+3ry' – 8y = 0. (a) Verify that the function y1 = x²…

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Q: 1. Solve the initial-boundary value problem du 0 0 3 dx2 u(0, t) = u (4, t) = 0 t 20 37Tx u(x, 0)…

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Q: Consider the following initial value problem: dy = -ty + dt 4t y(0) = = 1. Use the midpoint method…

A: The differential equation given is as follows: dydt=-ty+4ty Where ft, y=-ty+4ty. With the initial…

Q: Suppose that y and z are twice-differentiable functions of x. Show that d y dx y' 2 y"

A: Derivative of a function is the measure of how fast the function is changing with respect to the…

Q: Determine the domain and range of the given functions. Then sketch the contour plot of function…

A: We have to find the domain and range of the function fx, y=2y2+6x2+32+6. The domain of the function…

Q: Imagine a man on the grid below. A path is considered to be "valid' if it consists only "go right"…

A: Consider the given grid: Given that a man can go either right or up. Observe that a man can go…

Q: Drag the appropriate expression to complete the first step for writing an equivalent rational…

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Q: 2, Find bases for the fundamental subspaces; R(A), R(A"), N(A), and N(A"), given the matrix 1 -2 2 A…

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