Show that [1 1 0 0 1 1 0 001 1 0 det⠀⠀⠀⠀ ⠀⠀⠀⠀ 000 0 100 0 001 00 00 ⠀ ⠀| = 1+ (−1)n+1. ⠀⠀ 1 1 0 1

Q: 3 -7 [3] 7 -5 Let E= -2E= 0 Find -2E. 00 8 [000) 000 1000 [00] Undefined

A:

Q: 1-x We want to compute dr.

A:

Q: 86. Show that Z, = r(cose + isine) and Z2 = r[cos(-6) + isin(-6)] are conjugates. %3!

A: Given,

Q: (4) State which of the following statements are true, vacuously true, or false. (a) (A-B)' = A' -…

A:

Q: Find an explicit formula for 1/(2-1/2), 2/(3-1/3),3/(4-1/4),4/(5-1/5)...

A:

Q: Find sin(0) 13 12 O 5/13 O 12/13

A:

Q: Show that 1 0 1 0 0 1 0 1 00 1 det: ⠀⠀⠀ 000 1000 0 0 00 00 ⠀ ⠀| = 1+ (−1)”+1. 01

A:

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: Question 5. By choosing a specific "A(x)" over the natural numbers show that the claim in quotes…

A: Given,We have to choose a specific A(x) over the natural numbers. To prove that the theorem…

Q: Show that det [1 1 0 0 1 1 0 0 1 0... 0 0 1 ⠀ ... 0000 1000... 00 00 11 0 1 = 1+ (-1)"+¹.

A: As per the question we are given a matrix determinant, whose all diagonal and super-diagonal…

Q: Prove that 5"-4n-1 is divided by 16, where n is any natural number.

A: To prove that for any natural number then  is divided by .Definition of divisibility is if  then…

Q: Express in lowest terms. x+ x* x - x+ 1 ) 1+ x? O x(x + 1)

A:

Q: 9. Prove the following algebraic identity: (a - b)(a? + ab +b?)=a' -b'

A:

Q: Show that det [1 1 0 0 1 1 0 0 001 0 0 0 1... 0 0 ⠀⠀⠀ 0000 1000 0 0 ... 1 1 01 = 1+ (-1)"+1.

A: The given matrix is a circulant matrix with a special structure. A circulant matrix is a matrix in…

Q: lim,-1 f(x) =

A:

Q: (8) Let p = 7. Compute the index of a with respect to the primitive root g = 5 for a 1, 2, 3, 4, 5,…

A: We recall the definition and solve this problem.

Q: Evaluate 7/8 S 0 11√ 1- cos 8x dx либ

A: