Let A be an n x n matrix with eigenvalues A₁ and A2, where A₁ A2. If Sx, is the eigenspace associated with A,, i=1,2, then Sx, Sx₂ = {0}.

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Q: 'rove 1 det(A) = %3D det (41)

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Q: Show that the series 3. + + 4 To t (-1) Lonverges absolutely.

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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: Prove that AB #BA for [2 4 3 2] A = 1 1 0 3 14 6 2 5 B 1 2 0 315 3 2 4 L1 1 6

A: We have given two matrices A and B to prove that AB is not equal to BA.Matrixes are given below :

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Q: prove for all ne J, 1+ 3 + 5 +..+(2n-1) = n² by induction

A: The statement is for all To prove :The above statement is true using mathematical induction.

Q: QUESTION 9 Use Mathematical induction to prove that 2 divides n2+5n, n21.

A: Question 9: Let n=1 is true for Let the result be true for n=k,  We need to prove the result is…

Q: Find the d. c. of T from definition.

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Q: a) e +1 -6 -5 -4 -3 -2 -i 3 శ్రీ

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: By Principle of Mathematical Induction prove 6n 6

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Q: Prove NIn, +oo[= 0 ! n=1

A: To prove that ∩n=1∞[n,∞)=∅. Suppose that x∈∩n=1∞[n,∞). Then, x∈[1,∞), x∈[2,∞),.... That is, x≥n,…

Q: Prove or disprove 4|[(2²n-1 + 4)"]⁰

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Q: Prove 1 0, Ø ! n n=1

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Q: 1 Show that n2 + 1 IN V

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Q: Let n be a positive integer. Suppose that there are three pegs and on one of them n rings are…

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Q: Prove that 1.3 + 5.7 + 9.11 + =

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Q: n is not prime → 3n k < yñ

A: A number is said to be prime if it contains only two factors 1 and the number itself. Examples for…

Q: 1 41 7, then prove that A = A. -8 4 7. If A = 4 4 1

A: Given: A=19-8144471-84

Q: Prove gcd(n, n+1) = 1.

A: To prove the below expression. gcdn, n+1=1

Q: Find LV LV₂ hpæp(¿h+¿x)uis hæ

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Q: Q. Prove that by mathematically Induction 2" < (n + 1)! , for all integers n 2 2. а.

A: We Solve it by First Principle of Mathematical Induction.

Q: -x 0 if and only if x = 0. O Cannot be determined O False O True

A: Question 9 Given -x4 &gt; 0   ---(1) As  x4 &gt; 0 =&gt; -x4 &lt; 0   ---(2) So from (1) and (2) we…

Q: Prove that for every positive integer n the number (1 – /2)" is not ratioanal.

A: Given: The given number is, (1-2)n where n is the positive integer.   To prove: The number (1-2)n is…