If T: R"„8* is a Linear transfor matiom and m (x)= (2² +2)Cx+ 3. Find all the ratinal canomical ferm of T.

Q: The Critial Points of fcx,y)t+Ý-4y subject to the x+y=9 is O (o,さ3), (は5,2) ④ (e, さ)さ何,) None of…

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Q: Grplain why Ž diverges, 27 41 even though has a finite liniit 2 t 2

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Q: 2.4 (Ross, 2003, page 593) Show that the relationship $ (x) = x;¢(1;, x) + (1 – x;)ø(0¡, x) is true…

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Q: 6. Show that the sets S = (1,5) and T = (0, 00) are equinumerous by finding a bijection from S to T.…

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Q: A cubic spline S is defined by: So(x) = 3(x- 1) + 2(x – 1)² – (x – 1) S(x) = s,(x) = 4 + 4(x – 2) –…

A: Natural Cubic Spline is a piece-wise cubic polynomial that is twice continuously differentiable.…

Q: 5.Use thelefinition to Rrave that Jw wh- 2

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Q: . Finish showing the Complementary Slackness Theorem by establishing that under the hypothesis of…

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Q: Ex: O calkulake th gui for the disanse formula in a barred cordihute system defined by R = Ax, whene…

A: Here, one matrix function, A=1-223 is given Let the X=a1b1a2b2 So, X¯=AX=a1b1a2b2.1-223…

Q: 3- prove that w = w yx if w = xy² + xy +

A: Given problem:- w=xy2 +x2y3+x3y4  Prove that wxy =wyx

Q: Find the fowien senies fon | X), -T<X <A

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Q: verify that (A + B)T = AT + BT

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Q: Exercise 4 Show that for cach k EN it holds that kn-k < n! S n", Vn E N, n2 k. Deduce from this that…

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Q: In R, the model mod <- Im(z ~ x + y) will contain: O the results from regressing the dependent…

A: Introduction: It is required to identify the correct option.

Q: 8. Work out a Gaussian quadrature formula of the form Ans. A; = 1, x; = Aif(x1) + Arf (x2). f(x) dr

A: The given problem is to prove the following integral, the proof is to show the 2 point gaussian…

Q: Prove that ifx > 3 and y> 4, then xy > 11.

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Q: If the i, j entry of A is i times j, show that det A = 0. (Exception when A = [ 1 ] .)

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Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

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Q: If n > 2, prove that Q„ has at least n!/2 Hamiltonian cycles.

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Q: verify that (AT )T = A

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Q: ·[²₁₁-²² Compute (a) Trapezoidal rule de using the

A: Given integration is I=∫-11e-x2dx here f(x)=e-x2 For n=2 subinterval step size is h=1-(-1)2=22⇒h=1…

Q: 2. Solve the following Cauchy problem: xyu, + yu, + yu = y – x with 1 u = -- y = x². on

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Q: @ Let A -a Find Cenditiens on a,b.c and d that AX =o has infailely many Solution. what must there…

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Q: Compute the Wronskian, W[y1, y2](t).

A: Let y1(t) and y2(t) be two differentiable functions in the independent variable t. Then the…

Q: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

A: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

Q: c If in is an involution of X, show that (x, y)in = (yin, xin) is an involution of X2). %3D

A: Let X be a lattice We have to show that (x, y)in=(yin, xin) is an X[2] X[2] is a 2 x 2 matrix We…

Q: If a (b,v,r,k,lambda) design is symmetric with lambda=1, then there exists an integer n such that…

A: Using projection property in BIBD.  We know that, Symmetric 2-designs with λ = 1 and order n &gt; 1.…

Q: 3. 2. If A is 2x2 matri x aud Á = A, but %3D A+ A. show that A= 0

A: The solution is :

Q: 2. Use Wronskian to show that fi = x, f2 - Inz, and fa C (R). z Inz are linearly independent in

A: First we will calculate the wronskian of given functions f_1,f_2,f_3

Q: 3. Show that X = (x|Ax=b, x ≥ 0} is convex. following ure which no

A: As per our guidelines we are supposed to answer only one question.

Q: 2 Given u -1 and U , for which w is the set {u, v, w} linearly independent?

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Q: Let A find on Conditions a,bic and d has infinitely that AX =o many solution . what must there Pere…

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Q: Given: mAB = x Prove: mz1 = 180° - x A D Exercises 25, 26

A: Given:           m AB⏜ = x   To prove:              m&lt;1 = 1800 - x

Q: Is ZXZ cyclic? [Here Z means (Z, +).]

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Q: (a) express ux, u y, and uz as func-tions of x, y, and z both by using the Chain Rule and by…

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Q: graph the points z = x + iy that satisfy the givenconditions. | z |&gt; 2

A: Complex numbers

Q: Show that; is a linearly independent set in R3.

A: S=121,011,201 Let a,b and c be the scalar in R3. Then write the set in term of linear span.…

Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: onsider two points (x0, y0) and (x1, y1). Prove that the first order Lan￾grange polynonial is…

A: There are two points (x0 , y0) and (x1 , y1) ,now prove that the linear Lagrange interpolating…

Q: Show that the equadion Can also be obtaind from the fellowing squation 4(一 20 where and

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

Q: Exauple- If v=(T') is a contraviurient vecfor, Shew that He Parhil clenivatokes , dehined in each…

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Q: Show that S = 2 is a linearly independent set in R³.

A: Given:     S = 121 , 011 , 201   To show that S is linearly independent set in R3

Q: Show that if AT Ay = y for all y in Rn, then AT A = In.

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Q: 2. Use Wronskian to show that fi = x, f2 = ln x, and f3 C (R). x In x are linearly independent in

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Q: 1. Let A = and B = For what values of t is 2A +B invertible?

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Q: Compute the convolution y(n) = x(n) * h(n) , Where x(n) = {1,1,0,1,1} and h(n) = {1,-2,-3,4} , Using…

A: Given: Given convolution expression is Y(n)=x(n)*h(n) x(n)={1,1,0,1,1} h(n)={1,-2,-3,4}