Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is orthogonal to u. Enter them as 2x1 arrays into y_u and y_o respectively.

Q: 4. (i) Consider the 3 x 3 permutation matrix 0 1 0 P = |0 0 0 1 1 0 0 Find all 3 x 3 matrices A such…

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Q: Prove thatc "is a vector space over the field of real numbers as well, for any n

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Q: 2. At what point on the line y = b does the line segment from (0,0) to ( a,0) subtend the greatest…

A: at what point on the line y=b does the line segment from 0,0 to a,0 subtend the greatest angle.

Q: Erin, an lowa resident, has a personal auto policy with liability limits of $20,000/$40,000/$15,000…

A: Solution: $20,000, because that is the liability limit per person in Erin's personal auto policy.…

Q: Find the intervals of concavity and inflection ints of f. Sketch the graph of f.

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Q: 4. (i) Consider the 3 x 3 permutation matrix 0 1 0 0 0 1 1 0 0 P = Find all 3 x 3 matrices A such…

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Q: 1. An instrument store gives a 10% discount to all students off the original cost of an instrument.…

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Q: Show that the series 00 f)-Σε -" cos n *x n=0 is infinitely differentiable everywhere, but the…

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Q: Let V be the space spanned by f 1 = sin x and f2 = cos x. (a) Show that gi = 2sin x + cos x and g2 =…

A: Here we use the definition of basis of vector space is the smallest linearly independent set…

Q: Producing a vector vk= xk, xk+1, xk+2 and matrices A=PDP^-1, (vk+1=Avk), solve the linear recurrence…

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Q: II. Consider the function g defined by 1 g(x, y) = cos (Tx Vy)+ log3(x – y)' Do as indicated. 1.…

A: First we change the base if logarithm to e.

Q: Find the value of x for which Inx + (Inx)2 + (Inx) + (Inx)* += 9

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Q: 4) The curver= V1 + sin20,

A: Solution :-

Q: The function x2 f(x) = 1 - x is decreasing on (0, 1). Select one: O True O False

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Q: Let D-{tx.y.2) : 2+y?s2s 1, z2 o}. Evaluate z dv.

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Q: Find the value of c for which the vectors -2 and c-3 in R'are linearly dependent. Select one: 1 2 O…

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Q: Evaluate F. dS, S where F(x, y, z) = (3xz – Vy? + 2?, sin(x – 2), e" - z²) and S is the surface…

A: Since S is the boundary of closed region in space. So we apply the Gauss Divergence Theorem.

Q: S,x = - x+e"(1 – x) (c) Determine the following w-limit sets of (1): (i) w({0}), (ii) w((0, 1)),…

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Q: f the sum of the co-efficients in the expansion of (a + b)" is 1024, then the greatest co-efficient…

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Q: V=R Prooflthat Nisavectors sPoe

A: Here we use the definition of vector space and it's axiom to prove the question

Q: This answer is incorrect. :-(

A: Given that,r=6 ftR=12 fth=24 ftDensity of water=62.5 lb/ft3The work required tp pump the water out…

Q: Q4: Fill in the blank: If –3X + = 0, then X

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Q: a) Given the vectors in R3 v, =(11 -3), vz= (1 -3 1), v3=(-3 11) Using the system of linear…

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Q: Prove that 17 is the only prime number of the form n°- 64.

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Q: Consider the function g defined by 1 g(x, y) = sin (7/æy) + log3(æ – 3y)' Do as indicated. 1.…

A: gx,y=sinπxy+1log3x−3y

Q: Find the area of the plane region bounded by the given curves 1. y = x, y = 2x, and x + y = 6…

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Q: particular very sm alue of gross regionald n a

A: Given in a particular very small region, the consumer price index, C, depends on the currentvalue of…

Q: 1. E 3. Evaluate: lim ( -) X-0 \sinx

A: As per the policy of bartleby the provisions is to solve only one question at a time

Q: You have $400,000 saved for retirement. Your account earns 7% interest. How much will you be able to…

A: We have to solve the given problem.

Q: let t={usx8 x-uiscoantableiuioi then Tis called Tcof

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Q: Find the solution of the equation = e cos y dy? which tends to zero as x → 0o and has the value cos…

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Q: ĐUse the Fuler method's solve the: らゃう2び20 (o)1 れ:0r

A: We will use the formula of Euler method which is  yn+1 = yn + hf(xn , yn).  Then we will perform the…

Q: Let F be a subfield of the complex numbers, let f be a polynomial over F, and let f' be the…

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Q: Let E be the surface with equation (y – 4/2)2 1. | 32 52 42 (a) Give equations of the traces of E in…

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Q: Prove that Let T be a linear operator on V, and suppose that the minimal polynomial for T is…

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Q: 35) y+ y, =-5cos(2t), y+y, = 5cos(2t), y;(0) = y{(0) =1, y,(0) =-1, y,(0) = 1.

A: The solution is given as

Q: 3. Consider the vector space V p<? = {ax? + bx + c : a,b, c E R} of quadratic polynomials. Let B be…

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Q: 9B u- A2- (+4) + (+-2t)k aond V = Sintî + 3e-+ - 30ost e then bind (ůx) at-0 %3D the value ot d?

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Q: Q1: For the given matrix A, find (a) The rank of the matrix A, (b) a basis for the row space (c) a…

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Q: 9. Solve the given (matrix) linear system: [1 0 X' = 1 5 L2 4 -3] 1 X %3D

A: Solution :-

Q: The graph of a function f is given below. According to the graph, f"(x) > 0 on (3, o0). y y = f(x)…

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Q: need an example of a critical point of a nonlinear system of differential equations that satisfy the…

A: This is a question from stability analysis.

Q: Consider the double integral xy I dA x2 + y? R. where R is the region of the XY plane, given in the…

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Q: 1. Verify Green's theorem in the plane for $ (3x2- 8y,dx + (4y - 6xy)dy, where C is the boundary of…

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Q: FOURIER SERIES Find the Fourier series of f(x) as given over one period. Sketch f(x). (Show the…

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Q: t-a, - 10<1< 3 f (x) = 12+ at, 3<t< 10

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Q: , Does there exist an 8 x 8 matrix A = (as) satisfying the following three conditions? (i) If i 2 j…

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Q: 2 -5 Solve the IVP y' = || [ y(0) = | - ]. 2 cos t у + 1 -2 cos t

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Q: ) Express 8-x over Q[x] and over F2[x] as a product of irreducible ynomials.

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Q: 1- Use Euler Method to find value of y at x = 1.5 for the D.E. y' = x/y with initial value y(o) =…

A: We first find the solution by Euler method using the step size h=0.3 of the given differential…