Problem 4. Let A be an nx n matrix and S = {v1,. ., Vn} be vectors in R" such that Avk = \gV¢ for k = 1,..., n. Suppose that 0 < A1 < A2 < ..…< An. Prove that S is a basis for R".

Q: 2 excos2rdr / 2) 0

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Q: Show that (AB)¹ = BTA¹ if A = 2 0 2 0 and B = -1 1 15) -3 1 -1 -1 2 2). a

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Q: 1. Lat A - [; : - and B = 2 2 1 3 4 (a) Compute AB. (b) Compute BA.

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Q: 13) –3sec² 0+7=3

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Q: 13-Prove that a.b= la+bl²- la-bl²/4

A: a. b=[ la+bl2- la-bl2]/4Prove.