a) i) Give an inductive formula for the sum of the first n odd numbers: 1+3+ 5+ . + 2n -1 ii) Prove, using the inductive proof method, the correctness of your inductive formula in i) above. b) The...


a) i) Give an inductive formula for the sum of the first n odd numbers:<br>1+3+ 5+ . + 2n -1<br>ii) Prove, using the inductive proof method, the correctness of your inductive formula<br>in i) above.<br>b) The following program segment computes C = A * B, where A, B, C are matrices.<br>for (long int i = 1; i<= r; i++)<br>for (long intj = 1; j<= m; j**)<br>{<br>long double S = 0;<br>for (long int k = 1; k <= n; k++)<br>S = S+ A[i, k] * B[k, ];<br>Cli, ) = S;<br>How many times does the code iterate in computing<br>i) S?<br>ii) The j* column of C, i.e. C[i,j] for a fixed i and j = 1,2, ,3, ..., m?<br>iii) The complete matrix C?<br>

Extracted text: a) i) Give an inductive formula for the sum of the first n odd numbers: 1+3+ 5+ . + 2n -1 ii) Prove, using the inductive proof method, the correctness of your inductive formula in i) above. b) The following program segment computes C = A * B, where A, B, C are matrices. for (long int i = 1; i<= r;="" i++)="" for="" (long="" intj="1;"><= m;="" j**)="" {="" long="" double="" s="0;" for="" (long="" int="" k="1;" k=""><= n;="" k++)="" s="S+" a[i,="" k]="" *="" b[k,="" ];="" cli,="" )="S;" how="" many="" times="" does="" the="" code="" iterate="" in="" computing="" i)="" s?="" ii)="" the="" j*="" column="" of="" c,="" i.e.="" c[i,j]="" for="" a="" fixed="" i="" and="" j="1,2," ,3,="" ...,="" m?="" iii)="" the="" complete="" matrix="">

Jun 11, 2022
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