Find the multiplicative inverse mod n of x. Your answer should be an integer s in the range 0 through n - 1. Check your solution by verifying that sx mod n = 1. x = 52, n = 77 gcd(77,52)= O gcd (77,52)=1 with sequence of inverses: 77 52 25 2 1 O No answer text provided. O No answer text provided. O gcd (77, 52) = 52 sequence: 77 52 O No answer text provided. No answer text provided. O No answer text provided. O gcd (77, 52) = 77 sequence: 52 77 O No answer text provided. O No answer text provided. O No answer text provided. O gcd (77, 52) = 52.77 no sequence: O No answer text provided. O No answer text provided. O No answer text provided

noitulos wo mi This question concerns the following two subsets of R4: S = {(0,1,3,2), (1,0, 1, 0), (1,-1,-1,-1)}, four baus ein T = {(a, b, a+b+c, c): a, b, c ER}. yo restoodTebquargal elques 161) esin ein bos essoal? (a) Show that SCT, and write down a vector in R4 that does not belong to T. frus slunem 101) edmun Jan Boy Tod (b) Show that T is a subspace of R4. mudun edr (c) Show that S is a basis for T, and state the dimension of T. dead sout to amuoms sis to moite acper band-tigh y (d) Show that two of the vectors in S are orthogonal. Without using Gram-Schmidt orthogonalisation, find an orthogonal basis for T. mi sie od hirede show inanonob as el vie (e) Find an expression for the vector (3, 1,-1,-5) in T as a linearada yd combination of the vectors in your orthogonal basis for T. blods noY

(a) (b) S = 5 12 (0·0·000} 1 Is S a spanning set for R¹? Justify your answer. 10 7 Is S linearly independent? Justify your answer.

Linear algebra: please solve q20 correctly