Exercise 4 Let X andY be a normed vector spaces and let T: X → Y be a linear operator. Define ||2||a = ||x|| + ||Tæ|| V x € X. Show that, since |· || is a norm, ||· |la is also a norm.

Q: go SL x* dy- dy ax where L is segmeut bekueeu two pailuts (9,0) aud (1,0)

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Q: Example: Solve the following system of linear equations using Crout method. 1 1 -4 -1) x2 = (2 0 -1…

A: Given a system of linear equations                                                 4101-4-10-14…

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A: Given equation 2x312-30x8=0. We have to find the value of x. Zero matrix A zero matrix is just a…

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A: Solution : Given complex numbers  Z1 = (3 ,7) and Z2 = (-2,5)

Q: Question 4 Given that EF is the midsegment of trapezoid АВCD, what is AB? 92 cm D 12.6 cm

A: Given that EF is the mid segment of the trapezoid ABCD. We have to find the value of AB.

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A: The box plot is given about the height of boys and girls.

Q: 6. Find the Inverse Transform of F(s) S-8 3 A f(1) =6+e¬8 – 4e B f(1) =6-e"+ 4e* © s(1) = - 6+ e +…

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Q: By using Cauc hy laws find= Cos X.dx IT (x?+)) Sinx cos A) dx COS X e)

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Q: FALSE and give a counterexample and justify or explain briefly why this is such. (a) Let A and B be…

A: Here we use examples and theorems for sequences.

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Q: 1/4 1. Find all the values of 3.

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Q: Question A1 Consider a vector field F= 2x° yị +x'j., and a curve C defined by the equation y = 2x².…

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Q: 1. Use an alphabetic Caesar shift cipher with a shift of 6 right to encrypt the following message:…

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Q: 5. Consider the vector space P2 along with the subspace, H= span {1+ 21°, 2, -f,1-f} Use coordinate…

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Q: Find all roper nontrivial subgroups of Z; x Z, x Z. Find all subgroups of Z; x Z4 of order 4. Find…

A: Given:   subgroups of Z2 × Z2 × Z2.

Q: ) (4,0) ) (이14) ) (4,시) S. x* dy - 2y dx whare L is 2° J. circle arc x+y% =1, x >O X 70

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Q: f(t) = 2t² + 4t – 3 4+2s-3s? А. c 4+4s-3s? С. s3 2+2s-3s2 В. 2+4s-3s2 D. s3

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Q: =At iteration i=3, b .2 f (x) = x³ – x – 2

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Q: How much is the selling price of a gas stove listed at ₱2,650 if a discount of 15% was given to the…

A: listed Price(LP) = Php 2650  Discount % = 15%  Discount Price(D)= 2650×15/100 = Php 397.5 Selling…

Q: 4. у + 2x &y(1) = 2. y3

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Q: 3) Show that (a + bi)º = (a – bi). Hint: for any x, y in a field containing Fp, (x+y)º = xº + yP.…

A: As per our guidelines, we are supposed to answer only one question if there are multiple questions…

Q: Determine the value of the following mathematical expression, where u=3 and v=6. each) 4v a. w = Зи…

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Q: f(t) = te3t cosh 4t s2-6s-7 А. (s2-6s+25)2 s2-6s+7 С. (s2-6s-25)2 s2-6s+25 3. (s2-6s-7)2 s2-6s-25 D.…

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Q: Question 6. Given a group (G, *) and a nonempty set S. Let GS denote the set of all mappings from…

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Q: latiolis • find general solutions; • solve the initial value problem with initial condition y(0) =…

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Q: f(t) = t cos 4t 8s 8s А. (s² –16)? С. (s2+16)2 s2+16 В. (s2 –16)2 s2-16 D. (s²+16)²

A: To find the Laplace transformation.

Q: CustomerT batslgmos dmn svig ai a W Y Z. done 10 2 8 on 6. 4 12 8. 14 10 8 2 D 4 14 10 8. Тaxi

A: Hungarian  Method-2 :-

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Q: Eva receives utility from consuming burgers (X, the good on the horizontal axis) and orange juice…

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Q: If A is a square matrix such that A =1, then A'is equal

A: Given, A is a square matrix such that A2=I.

Q: f(t) = e4t cos 3t 3 s-4 A. s2-8s+25 С. s2-8s+25 3 s-4 В. s2-8s-7 D. s2-8s-7

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Q: (y – x)dx + (y + x)dy = 0.

A: The given differential equation is ;                      (y-x)dx + (y+x)dy = 0 We have to solve the…

Q: 6. Simplify. Write as a mixed radical in lowest form. V300 – 5/27 + 2/12 - [5,5] a) b)

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Q: of all sequences that are "eventually zero," that is, al

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Q: Using the theorem on determinants, show that a a? b b2 1 |1 A = 1 (b – a)(c – a)(c – b) - C

A: We have to show that A=1aa21bb21cc2=(b-a)(c-a)(c-b) by using the theorem on determinants .

Q: Problem 1: Given: -2,3,8, 13, ... Find the following: (a) 6th term of the sequence; (b) an formula…

A: Here we use arithmetic progression.

Q: Find all the solutions r E Ziz to the equation r³ – 5x² – 7x = 0 mod 13.

A: First, solve in real number then ring down to the finite field.

Q: You have just sold your house for $1,100,000 in cash. Your mortgage was originally a​ 30-year…

A: Given: n = 360 FV = 0 PV = 750,000 rate = 5.25%/12 = 0.4375%

Q: 1- Evaluate without a calculator. Show your work. a) Log 0.000001 b) log4 (1/16)* 33 51/4

A: The given problem is to evaluate the given logarithmic terms. Given logarithmic terms Log(0.000001)…