4. Create a function, which, given an input of a positive integer n, produces an n...

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4. Create a function, which, given an input of a positive integer n, produces an n x n matrix A = (Aij) such that Aij=i+j-1. For example, the function should return a matrix below with an input n = 5. 1234 1 3 4 5 456 4 5 6 7 5 6 7 8 9 2 3 5 6 7 8 Hint: Using rep() and seq() as needed, create the vector 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 and vector 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 first. 1. (a) Learn function plot () by running commands x < 1:100 plot (x, 1/x, type='1') (b) Calculate the sum for all n between 1 and 100. Plot the sum versus n. =112 (c) Calculate the sum Σfor all n between 1 and 100. Plot the sum versus n. (d) (*) If you increase n, what can you say from the graphs about convergence of the series? (This is an optional question. No credit.) 4. Create a function, which, given an input of a positive integer n, produces an n x n matrix A = (Aij) such that Aij=i+j-1. For example, the function should return a matrix below with an input n = 5. 1234 1 3 4 5 456 4 5 6 7 5 6 7 8 9 2 3 5 6 7 8 Hint: Using rep() and seq() as needed, create the vector 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 and vector 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 first. 1. (a) Learn function plot () by running commands x < 1:100 plot (x, 1/x, type='1') (b) Calculate the sum for all n between 1 and 100. Plot the sum versus n. =112 (c) Calculate the sum Σfor all n between 1 and 100. Plot the sum versus n. (d) (*) If you increase n, what can you say from the graphs about convergence of the series? (This is an optional question. No credit.)

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Objective To create a function which given an input of a positive integer n prod... View the full answer