Answer with reason plz
(t) (T, F) If AB = I, then B = A−1
(u) (T, F) The congruence equality 6n ≡ 5(mod 8) has no solution.
(v) (T, F) 5 is an inverse of 10 modulo 7.
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6.32 Theorem. If k and n are natural numbers with (k, d(n)) =I, then there exist positive integers u and v satisfving ku=(n)u The previous theorem not only asserts that an appropriate exponent is always availahle, but it also tells us how to find it. The numbers u and are solutions lo a lincar Diophantine cquation just like those we studied in Chapter 6.33 Exercisc. Use your observations so far to find solutions to the follow ing congruences. Be sure...
Modern Algebra, MAT 401 Test 3. Show your work (b) 1. Find a solution x E ZOSXsn for the congruence (a) 8x+3= 5 mod 9 8x=l(mod 21) 2. Find the least positive integer that is congruent to: (a) (14+46+65+92Xmod 11) (b) (717)(32)(62)(mods) (c) 62(mod5) 3. Solve the system (a) x = 2(mod 5) em a lx = 3(mod 8) x 4(mod 7) (3x + 2 = 3(mod 8) 4. Solve the system (a) [4][x] + [2][y] = [1] () {[3][x]...
please solve, previous ones all wrong! Question 11 1 mark) Attempt 2 What is the Inverse Fourier transform of F(u)- 10-5? Reflection: F-1[F(-u)]=f(-t) Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t) Question 12 (T mark) Attempt 2 What is the Inverse Fourier transform of: 7 16+iw-4)2 Reflection: F--) Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t) Question 13 (2 marks)...
Numbers 3,4,11 a. SublactiTlnb b. division of nonzero rationals c. function composition of polynomials with real coefficients d. multiplication of 2 × 2 matrices with integer entries e. exponentiation of integers 3. Which of the following binary operations are commutative? a. substraction of integers b. division of nonzero real numbers c. function composition of polynomials with real coefficients d. multiplication of 2 × 2 matrices with real entries e. exponentiation of integers 4. Which of the following sets are closed...
(b) The signal f(t) is shown in the figure below 3 2 f(t) _ 0 I 1 -4 -3 -2 -1 0 1 2 3 4 5 6 7 t and is given by 21 (1) + 3A (132), where A is the triangle function defined as 10-{ It a It <a It > a 0 Write the Fourier transform F [A(t)] (s) of f(t) exploiting the fact that FA(t)](s) = sinc-(s) where sin(TTS) sinc(s) ITS and the theorem for...
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped a Screen Shot 2019-05-17 at 2.07.40 AM Search Question 14 (2 marks) Attempt 1 Find the inverse Fourier transform of: F(w-5 π w sgn(w) e-Tw Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped Question 15...
I need help with number 3 on my number theory hw. Exercise 1. Figure out how many solutions x2 = x (mod n) has for n = 5,6,7, and then compute how many solutions there are modulo 210. Exercise 2. (a) Find all solutions to x2 +8 = 0 (mod 11). (b) Using your answer to part (a) and Hensel's Lemma, find all solutions to x2 +8 = 0 (mod 121). Exercise 3. Solve f(x) = x3 – x2 +...
solution help, tq. What is the Inverse Fourier transform of Your answer should be expressed as a function of t using the correct syntax. Inverse FT. is f(t) = Skipped F(u)-(15ru2 +4ιτω4)sgn(a)? Find the Inverse Fourier transform of: F(u)--8πΗ(w+5)-H(w-5) e- Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is ft)Skipped 8iu Find the Inverse Fourier transform of: F(w) 16 πυ) sgn(w)e-20 Your answer should be expressed as a function of t using...
Please Do it clearly and ASAP UNIC HaHdheld ull, 130 points is a "perfect" score. Good luck! Part I. True False. Circle T if the statement is always true, and F if the statement is at least sometimes false. [10 pts] 1) T F RREF(A) is unique. 2) T F The solution set to "Ax b" is a vector space. 3) T F Every square matrix is diagonalizable. 4) T F Adding a column to a column of annxn A...
Please answer question 3 Find all (infinitely many) solutions of the system of congruence's: Use Fermata little theorem to find 8^223 mod 11. (You are not allowed to use modular exponentiation.) Show that if p f a, then a^y-2 is an inverse of a modulo p. Use this observation to compute an inverse 2 modulo 7. What is the decryption function for an affine cipher if the encryption function is 13x + 17 (mod 26)? Encode and then decode the...