[an] 2. If A is similar to a diagonal matrix D then A is similar to AT.

Q: s transformed it the Origin is si to the point (2-3) the axes reamining parallel to the original xxf

A:

Q: Suppose that E is an extension of F and a, b ∈ E. If a is algebraicover F of degree m, and b is…

A: Given that K is an extension of F and a, b∈E is the algebraic element of degrees m and m. Where m…

Q: The characteristic polynomial of A 1 -2 1 € M3(R) is p(A) = −X(X+3)². 1-2 1. Find the set of…

A: A=-2111-2111-2pλ=-λλ+32=0

Q: 1. If A is nonsingular then [adj(A)]-¹ = adj(A-¹). 2. The linear system AX = B has a solution if and…

A:

Q: Given a compact set A and a closed set B. ShOw that AB is compact!

A: A is a compact set B is closed

Q: Let b be a zero of f(x) = x5 + 2x + 4 Show that none of √2, ∛2, ∜2 belongs to Q(β).

A:

Q: If P divides OA internally in the ratio ?\index{1}:?\index{2} and Q divides OA  extrnally in the…

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

Q: = √₂ + 2dX = 0 + 2* Vo 0.5 as = v₁ = (v₁³²) 8.89*107

A: We are given v12=0+2×7.9×1016×0.05 We have to find the value of v1

Q: Write x7 - x as a product of linear factors over Z3. Do the same for x10 - x.

A: Given: Z3. To Do: We have to write x7-x and x10-x as a product of linear factors over Z3.

Q: x²-2 2²-1 - Let f(x)= (a) Find the domain, the intercept points and the asymptotes. (b) Find the…

A: We can find the given term.

Q: Consider R³ together with the standard inner product. Transform the basis {(1, 1, 1), (0, 1, 1),…

A:

Q: Consider the series ∞ k=1 1 k² (k+1) (i) Use Test for Divergence to check if the sequence is…

A:

Q: Find the Fourier series of the sign function f(x)=signx={−1,−π≤x≤01,0<x≤π, knowing that the…

A: Given: fx=signx=-1-π≤x≤010<x≤π We have to find the Fourier series of the given function.

Q: Let Show f is defined for all x > 0. Is f continuous on (0,∞)? How aboutdifferentiable?

A: Given: fx=1x-1x+1+1x+2-1x+3+1x+4-... To Show: Function is defined for all x>0 also explain…

Q: Determine whether the relation is a function. Identify the domain and the range.…

A: Here, we have to determine whether given relation is function or not, and also we have to find…

Q: 3 Prove that 11gx11² Show that Mis finite dimensional Vector sob space with dim (M) SAR (vse…

A: As per the question we are given a closed vector subspace M which is contained in C[0, 1] Now we…

Q: AB is a variable line sliding between the coordinate axes in such a way that A lies the x-axis and B…

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Q: Problem 2. Let C([0, 1]) be the set of real continuous functions on [0, 1], induced with the norm…

A:

Q: Prove the function is convex function T f(x, y) = log (ex+ey) where x, y € RT E

A: fx,y=logex+ey

Q: 26. Let a = (a₁,a2,a3,...,an) be an n-tuple of positiv ■d (w₁,w2,W3,..., Wn, ‚wn) be another n-tuple…

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Q: 23+13 23+1 :

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Q: How are the eigenvalues of AH related to the eigenvalues of the square matrix A?

A: Given: The eigenvalues of AH and the eigenvalues of the square matrix A.To find: The relation…

Q: Show by example that Σ(an/bn) may converge to something other than A/B even when A = gan, B = Σbn ≠…

A: Given that an, bn≠0 Let us consider ∑an converges to A. Also ∑bn converges to B. To show that ∑anbn…

Q: Show that the point of intersection of two lines in the plane of afield F lies in the plane of F.

A: Give that two lines in the plane of a filed F. We have to show that the point of intersection of two…

Q: Let α be a zero of f (x) = x2 + 2x + 2 in some extension field of Z3.Find the other zero of f (x) in…

A: Given: α is a zero of fx=x2+2x+2 in some extension field of Z3. We have to find the other zero of…

Q: on metho partial pivoting, the following system of equations : x+y+z = 7,

A:

Q: 0. 4 4t cos3t di

A: ∫0π/44tcos3tdt

Q: If V is a vector space over F of dimension n, prove that V is isomor- phic as a vector space to F" =…

A: Proving that two vector spaces are isomorphic involves finding a bijective linear map between them.…

Q: i : N → P(N) defined by n→ {1,2,...,n}. i is injective but not surjective Oi is surjective but not…

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

Q: A beautiful flux integral Consider the potential function p(x, y, z) = G(p), where G is any twice…

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: ind the general solution for  Z_yy +Z=e^(x+y)

A: zyy+z=ex+y

Q: nsider the following function: a) Find: 1) 01 2014 3) a2f ахду a2f дудх 5)011 = 4) b) Solve aly ola…

A:

Q: Determine whether or not the set is linearly independent over Zg.

A: Given set is S=2110, 0112, 1111 over Z5. We have to determine whether a given set is linearly…

Q: f a, b, c are positive real numbers such that a + b + c = 1, prove 8 8abc 27 (1a) (1 - b)(1 − c) ≤ -

A:

Q: Let F = Z2 and let f (x) = x3 + x + 1 ∈ F[x]. Suppose that a is azero of f (x) in some extension of…

A: Given: F=ℤ2 and a is a zero of the polynomial fx=x3+x+1. We have to: (i) Find number of elements in…

Q: Determine the ratio in which the line 3x+y- 9 = 0 divides the segment joining the points (1,3) and…

A:

Q: a. At what point should the origin be shifted if the coordinates of a point (4, 5) become (-3, 9)?

A:

Q: You are given the following system of equations:  x1 - 2x2 + 2x3 = 1, -3x1 - x2 + x3 = 4, x1 + 5x2…

A: The given problem is to find the solution for the given system of linear equations by using the…

Q: Consider the equation: 2sin(x) +2cos(x) = ² + x³ 1. Find the fourth approximation x, of the root in…

A:

Q: Given that A1,A2,A3,... An are n points in a plane whose coordinates are (xl,yl), (x2,y2), (xn,yn),…

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Q: If a and b are constructible numbers and a >= b > 0, give a geometricproof that a + b and a -…

A: Given that a and b are constructible numbers and a≥b≥0. It has to be shown that, a+b,a-bare…

Q: Evaluate the following integral : L² 1 (x³ + 2x) ex² dx

A:

Q: the probability that scientists from Area 51 will begin selling pet aliens in the next month is 38%.…

A: The probability that scientists from Area 51 will begin selling pet aliens in the next month is…

Q: 6.26 Determine the most probable length of a line AB, the standard deviation, and the 95% error of…

A: In this problem, we are given a series of observations of the length of a line AB that were made…

Q: Justify if it is true: If:TW a linear transformation, then Nuc (T) = T-¹({0})

A:

Q: 0 -2 € M3(R) is f(x) = -(x - 1)²(x - 5). 0 IV. The characteristic polynomial of A = 0 3 0-2 3 1.…

A:

Q: Show that every element of GF(pn) can be written in the form ap forsome unique a in GF( pn).

A: Given: GFpn. To show: Every element of GFpn can be written in the form ap for some unique a in GFpn.

Q: find the general solution for  U_xx =xy

A: Given: The given differential equation is Uxx=xy. To find: We have to find the general solution of…

Q: Prove that for x > <1+ ax, if 0 < a < 1, 21+ ax if 1 < a <∞o.

A:

Q: Give an example of a unique factorization domain with a subdomainthat does not have a unique…

A: To Give: An example of a unique factorization domain with a subdomain that does not have a unique…