1. Prove that for any natural n the following holds 1.2+2.3+...+ (n – 1) · n = (п — 1)п(п + 1) 3 2. Prove that for any natural n the following holds п (2n – 1)(2n + 1) 2n +1 1.3 3.5

Q: This is an algebra question.  A and B have to be equations..

A: Let's solve.

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A: if matrix are equal then crossponding entries will be equal

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A: To find the given values

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A: Solve the augmented matrix in the following way:-

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A: Given below the detailed solution

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A: Inverse: A matrix B is said to be the inverse of the matrix A if AB=BA=I, where I is the identity…

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A: Since you have asked multiple question, we will solve the first question with three subparts for…

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A: Sol Correct option :-

Q: If then and A = -4 2 2 2 -1 -3 AB= BA= -3 and B= 0 4-41 2 0 4 -3 0

A: If A=-42-222-3-1-3-1 and B=04-4204-301then to find AB and BA.

Q: [1 2 31 If A = 1 2 4 find A-1 li 3 4]

A: We find inverse of Matrix A by cofactor method

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Q: 11. (a-b)³ +3ab(a-b) a²+ab+b² a. b. a-b C. a+b a²+ab+b² e. b²-a a²+ab+b² d. ab is equal to: not in…

A: We will find the required.

Q: {X+Y=3 {2x+4y=8   {8x-7=-2 {-2-3y=10 These are 2 different questions

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Q: Solve the following а. х-4 2 3 3 b. х-2-1 <1 2 2

A: We solve given inequality

Q: O 7/1 - OO M8 7/43

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Q: 2 Give examples of sequences, one in each case, of the following. (a) (an) is unbounded and not…

A: Since you have asked multiple questions, we will solve one question for you. For other question,…

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Q: Find L - (8+3)3] 7 12 O 9t%e-3t O 6te3t O 6t?e-3t O 6t2

A: Use property of inverse laplace transform

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Q: Problem 4 (6.EE.A.3) Which expression is equivalent to 5(4x+ 3)-2x? A. 18x+15 B. 18x +3 C 7x+8 D.…

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Q: O -2 1 -1 A = 2 and C = 1 1 2 -1 -1, 4A + 0.5C

A: Give matrices are, A=0-22021C=1-111-1-1 Multiplying matrix A with 4. 4A=40-220214A=0-88084

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.