Show that [1 1 0 0 1 1 0 0 001 1 det ⠀⠀⠀N : ⠀⠀⠀⠀ : 000 0 100 0 ⠀⠀⠀ ... 0 0 00 00 ⠀ ⠀ = 1+ (−1)n+1. : 1 1 01

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: 1 1 1| 1 1 If A =|1 1 1], then A2018 = A?

A:

Q: Let A = 0 -5 1 C. A-1 a. det (A) b. 7A + 5I = || d. AB = - 2 - 3 0 = e. BT AT = -5 1 – 1. and B = 16…

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Q: * Evaluate. 2t |4 + et| dt

A: Solution :-

Q: Prove that if n is a +ive integer,

A: Given that, M xddxnf(x);p = (-1)npnF(p) We can prove this by mathematical induction.

Q: 1 1 1| 1 1 1 If A =|1 1 1|, then A2018. _A?

A: Here given matrix is  A=111111111

Q: Prove that _f₁ = = ₁+2 +851+1 −85₁-1 + ₁-2 +0(hª) 12h

A: Use taylor series expansion to prove this

Q: So [3/x] dr

A:

Q: 5 4 d.x x2/3 Evaluate I = 1 – x²

A: Indefinite integration

Q: (b) Let A¡ = [-i, 1] for every positive integer i. Find U A¡ and N1 Aj.

A: Given that Ai=-i,1 for every positive integer i. That is, A1=-1,1, A2=-2,1, A3=-3,1 and so on. To…

Q: antip . Prove that 4" -3"-7 is a multiple of 84 for each positive even m.

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Q: J0 ex' Evaluate 1 3* Sdx. 0 ex O 3.16 O 2.74 O 2.54 O 1.05

A: We need to find value of ∫013xexdx

Q: Q1 If A 010 1 Par API AYA² KA ナ show That:

A: If , show that .

Q: Which of the following is the graph of the piecewise function f (x) - 7 f(x) -2-1 2 1 √-x-1 if XS-1…

A: To plot the piecewise continuous functions: f(x)=-x-1 if x≤-1xx2-x-2 if -1<x<2log2(x-1) if x≥2

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

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Q: et A = -5 2 3 −1 -2 5 and B = -4-3 4 28 -6 -1 4 - 3 -5 20 -15 a. det(A) = b. 7A+41 = -10 -5 -15-25…

A: Since there are more than three sub parts , according to the guidelines, I am solving only the…

Q: A. 2.125 B.0 Rational 15 D. Integers E. F. 0.4 Whole G. 23 H. -1 Irrational Natural 16 L. V25 J. -49…

A:

Q: S[e²t. √4+e²] dt

A: Evaluation of the indefinite integral, by using substitution method

Q: 1. (a) 2 Let = (1, 0, -2) and = (-4, 2, 3). Find a real number x such that (ট' –æè) ⊥ à. (b)-1 (c) 3…

A: Let .To find a real number  such that .

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: 'evaluate the answer wItho 274/3

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Q: Given (34)-¹ = [3¹] 3¹, find A.

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Q: (1+a-c), (c) ₂F, (_n,‚a+n;c;1)=(-1)" !

A:

Q: f(x) = alog,(cx d) the x -axis and the line x = 9 using Midpoint Riemann Sum with 8 equal intervals…

A: 1st we will find range of blues of x and then divide it into 8 sub interval. Then apply mid point…

Q: Which of the following is NOT true about the DE: 6x²ydx +2x*dy=0?

A:

Q: 2. Find A if (A-1-21)² = -2 = -21]

A: Basic properties of matrix are used

Q: 2 3/2 + x² – 3x + 1 3 f(x) = 5x4/3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Compute L(t.s) for any positive integer n.

A:

Q: [1 2 If A =|1 then dim ((col (A))-) is 1 0. 2. 3. 1. O O

A: