Show That R is Banach Sface.

Q: what is reflexive Banach space ?

A: Banach space: A normed linear space N,· is called banach space if it is complete metric space. A…

Q: Prave R is banach Space with explanation.

A: Banach space: A complete normed linear space is called Banach space. Given:  To show:  is Banach…

Q: If A+ iB is Hermitian (A and Bare real) show that [ AB -BA] is symmetric.

A: As per the question we are given two real matrices A, B such that (A + iB) is Hermitian. Now we have…

Q: For a,bEN define the relation a -b if and only if ab is a perfect square. Is this relation…

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Q: If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(-3)g(-3)…

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Q: Let A be an n × n symmetric negative definitematrix. Show that the leading principal submatrices of…

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Q: Does the following set of polynomials {t? + 1, t2 + t,t + 1} span P2?

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Q: Show that R is not compact.

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Q: Let a, b, and c be distinct real numbers. Show that…

A: Consider the equation: We have to check whether it is a zero polynomial, symmetric and bi-linear or…

Q: 9. Find bijective functions from R to R a) f (x) = 2x + 1 b) f(x) = x² + 1 c) f (x) = x³ %3D x2+1 d)…

A: As per our guideline we are allowed to do 1 question or maximum 3 subparts at a time. Please post…

Q: give a clear and detailed proof of the following: if f: A implies B is a bijection, then f-1 : B…

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Q: Give example T2 space but not T3 Space

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Q: Calculate the commutators [p(hat)x3, x(hat)].

A: We have to calculate the following commutators. p^x3 , x^ Introduction: Commutation of operator A^…

Q: Let f be the function from {a, b, c, d} to {1, 2, 3, 4} with f(a) = 4, f(b) = 2, f(c) = 1, and f(d)…

A: For bijection, the function needs to be one to one and onto.

Q: В 3 {vi %3D (2, —2, 1), 22 —D (1, —3, 2), 1з 3 (-7,5, 4)}

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Q: 6) Suppose that an operator T on a complex vector space has characteristic polynomial t3 (t – 2)5 (t…

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Q: Define g : (-1, 1) → R by g(x) 1- x2 " Show that |(-1, 1)| = |R| by showing that g is a bijection

A: Concept Used: For a function f:A→B If f is a bijection, then |A|=|B| Consider the function g:(-1,…

Q: For an integer t, prove that gcd(2t + 1, 9t + 4) = 1.

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Q: Show that  ℝ2 = span([1 1], [1 -1])

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Q: Consider the system below. * = rx + y – x³ jy = -x + ry – 2y Chis system has a fixed point at (0,0).…

A: First we will calculate Jacobian matrix at the origin and then its eigenvalues. Then depending on…

Q: Quertion:- Show that R is a Banach Space.

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Q: Show that the glosp of bncar bijections ftom f5 faom f5 whes fis afjeld in isomaphic with GLI5f)

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Q: 2. Let A, B, C, and D be four groups such that A-C and B D. Show that A x B Cx D.

A: We will use the face that A isomorphic to C  and B isomorphic to D to prove the asked result.

Q: Determine the value(s) of x such that -2 -3 27 2 1]|-3 -3 3 [이 -1 2 18 5 Note: If there is more than…

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Q: Show R³ is a banach space.

A: Banach space: A complete normed linear space is called Banach space. Given: To show:  is a Banach…

Q: Consider the relation R on Z with rule (a, b) in R iff a + 2b is even. Is R reflexive, symmetric,…

A: We have to Consider the relation R on Z with rule (a, b) in R iff a + 2b is even.  We have to check…