6) Let S be a symmetric, invertible matrix and let M be an invertible matrix of the same size as S. Prove the following: T 1 M¯¹ (S¯¹) "'S(SM²) ¹ = S

Q: = Solve the matrix equation AX = B for X. 14 -4 B= A=[-33] ³- (-22) -8 X=

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Q: = (4) Let ER and fn = XAn, where An j+2k = n. Compute fe fn in terms of k and show that (a) the…

A: Pleas find the attached answer

Q: So the maximum is (-0.5, -16e^(-1))? And the minimum is (0.5, 16e^(-1))? I need the answer in…

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Q: On the Richter scale, the magnitude M of an earthquake depends on the amount of energy E released by…

A: If log a=b, then a=10b. The equation is provided as: M=23logE1011.8.

Q: e 6 Consider the integral dx with n = 4. X 1 a. Find the trapezoid rule approximations to the…

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Q: For the function f(x)=1/16x​, construct and simplify the difference quotient f(x+h)−f(x)/h.

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Q: A) What percent of the grid is shaded in yellow? 54 B) Assume the Area of the entire grid is 27 sq…

A: We see that there is 10*10 grid. So there are total 100 small squares.

Q: EXAMPLE 1. Use Inductive Reasoning to Predict a Number Use inductive reasoning to predict the next…

A: Given  First term a1=3 Second term a2=6 Similarly a3=8, a4=12, a5=15 a1=3        =2+1+12a2=a1+3…

Q: Find a basis of the subspace of R³ defined by the equation 2x1 + 3x2 + x3 = 0.

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Q: 4. You are given the following function f(x) sin(a), 0≤*S*. Using an even periodic extension, find…

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Q: (d) Let F be a field, R a nonzero ring and f: F→ R be a surjective homomorphism. Then prove that f…

A: 4(d). Given that  F  be a field, R a nonzero ring and f : F → R be a surjective homomorphism.…

Q: dy dz = 1+ 2z-y, y(0) = 1. (a) Use the Euler's method to find the approximation of y(2) with the…

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Q: O Solve the following initial value problem: dx dt dy dt = = 2x + 5y 2x - y x(0) = 1, y(0) = 6

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Q: 1. 2p-2 = ¹+¹ (mod p) p+1 2. (1.) k = 0 (mod p), whenever k = {1, 2,. ,p-1}

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Q: Solve the followig non linear. gebraic equation to fined al one non Zevo root. P(x) = Sin [√ Secx +…

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: a. What is the trapezoid approximation with n subintervals? T(4)= (Round to six decimal places as…

A: Let the given integral  I=∫1e6xdx   Take y=fx =…

Q: 2) Consider the DE: (2xy - 6x²)dx + (x² +9)dy = 0 A) Determine whether the DE is exact or not, then…

A: as per Q&A rules we have to answer only one question, when there are more than one different…

Q: Which of the following is NOT a differential equation? Select one: O dy dt = 3y = 2x²y + y² = 6 d²y…

A: A differential equation can be defined as an equation that relates one or more unknown functions and…

Q: Find the critical points of the function +2x f (x) = f±2 (t² − 1) et dt. Determine whether they -2x…

A: To find the critical points of the function and also determine whether they are minimum, maximum,…

Q: sin x dy dx dy +ycosx + 2xe³ − 3x² = (1 − x²e³) - - dx

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Q: Question 1 Assume that a sequence (fn)n of integrable functions converges strongly to an integrable…

A: please find the attached solution

Q: Find the matrix that produces the rotation.60° about the y-axis

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Q: If the price of gold decreases at a monthly rate of 2.2%, by what percentage does it decrease in a…

A: Given  monthly rate of decrease =2.2% Let initially the price be p0 and the price after 12 month is…

Q: 1-dx the Comparison Test. 4 Given that -dx converges, how do we know that We cannot compare 00 1 x³…

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Q: A mirror and a source of light are situated at the origin O and at a point on OX, respectively. A…

A: Let the co-ordinate of the source of light is Xa,0,0 where a≠0 The mirror is at origin that is at…

Q: (2) Let fn(x) = X(0,n)(x), x > 0. Find the pointwise limit f of (fn)n and show that (a) the…

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Q: Use two-timing (or averaging) to obtain the general solution of ï+ ε(x² + x² − 1)i + x = 0 with…

A: Please find the attached solution

Q: Describe the transformation having the following matrix 1000 0200 0010 4001 Dilation by a factor of…

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Q: How many integers in between 1 and 3000, inclusive are divisible by either 5 or 7?

A: Let A and B are two sets such that then number of elements in A and B are obtained as…

Q: Determine whether or not the following set of vectors span R³, (i) {(1, 1, 2), (1, -1, 2), (1, 0,…

A: Span of R3 .

Q: A) Solve the linear system x1 + 3x22x3 4x1 + 2x2x3 4x13x2 + 3x3 - 2x4 = 4 = 4 -2 using the…

A: (A)  Express the given system of equations in matrix form as AX=B then the augmented matrix of the…

Q: AN Solve the following to find one real non zero root: non-linear algebraic equation f(x) = sin…

A: The given functon is,fx = sinsecx +x3 e5xtanx -e-x To find: One non-zero real root of the  above…

Q: Condier that is the centre of a group F, So prove that > M(x) = F. and prove that if Fis finite,xe…

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Q: M 1 {[1 '* . _ (w/wn)²]² + [2¢w/wn] 1/2 2 1²}' ||

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Q: Find the family of graphs G of order p such that y(G) = p.

A: Please find the attached solution

Q: (a) Show that S is path-connected, by constructing for any two points x, y € Sn an explicit path…

A: please find the attached solution

Q: ength of any edge of a regular tetrahedr ar tetrahedron). Show that the angle bet

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Q: Can you write more clearly what you did in step 2? It is not clear to me.

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Q: Problem 4 Find the Fourier coefficients a, and ak of the following waveform X(t)=2t 0<t<1 -2 -1 x(1)…

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Q: Problem 4. Let (X, dx) and (Y, dy) be metric spaces. Show that the sup norm metric do we defined on…

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Q: Find the eigenvalues and eigenvectors for A = -[ 5} 11 60 -6-25

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Q: Consider the sequence (an) given by the recurrence an+1 = 2an-n for all n € N, with the initial…

A: We will find the pattern of a1,a2,.....,a6, the we can predict the general formula.

Q: the equation to the plane in the new position is ax + by ±z √√a²+ b² tan α = 0.

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Q: find the inverse function for the following function(those are all bijective func- tion) (a) f(x) =…

A: Note- Given that All function are bijective.

Q: show that Beltrami-identity does not help you. to solve the equation- + wint fo of t. show

A: Please find the attached solution

Q: sider the discrete-time LTI system -8y[n] + 2y[n 1] + y[n − 2] = −2x[n] + 3x[n − 1]. Find the…

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Q: (b) Let I, J be ideals (two-sided) of a ring R and check as to whether In J is an ideal (two-sided)…

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Q: find x, y € Z such that 2261x + 1275y = gcd(2261,1275).

A: we want to find the greatest common factor  we will use Euclid's algorithm 2261=1275×1+986 -----1)…

Q: In the figure above, if - what is the value of r? r=

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Q: Consider the following initial value problem. y" + 6y' + 25y = 8(t) + 6(t5a), y(0) = 1, y'(0) = 0…

A: Formula of Laplace transformation…