1 6] 3 8 Find formulas for the entries of M", where n is a positive integer. Let M MT- = I

Q: Let yk = k", where n is a positive integer; then Ak" = (k + 1)" – k" - (1.112) nk"-+ n kn-2 +...+ 2.…

A: We have to solve given problem:

Q: 7. Use the PCI to prove the following properties of Fibonacci numbers: (d) (Binet's formula) Let o…

A:

Q: Let Find formulas for the entries of M", where is a positive integer. M" O M -2*5**n 10 5 -5*n

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Q: 12 y 2 4xy³z² 4877

A: formula used  xa×xb=xa+blet  A=12x4y8z74xy3z2

Q: 1 1] 050 by expanding 7. 1. Compute det A, where A = %3D -1 7 2 a. On the first row b. On the third…

A: A=711050-172 a). By expanding along first row, we get…

Q: 6.) Derike the binomial idendity nent) (un-) C Hint: For mzz, c^)+2(^) +m?]

A: To derive the binomial identity22+42+62+.........+2n2=nn+14n-16

Q: 6 -1 Let A =| 0 -2 and B . Compute (AB)". Show your work. 4 3

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Q: Show that — ф+1 n=0 ||

A: Given φ is the golden ration satisfying 1φ=φ-1. To prove ∑n=0∞1φn=φ+1 It is known that φ=1+52.

Q: [2x-1]=-1 with an ε = .01, implies a 6 = .005 1-0 O True O False

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Q: Ifx+y+z= 1 and x, y, z are positive, then show that ( 1)² ( 1)² ( 1)² 100

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

A: