9. Determine the complexity of the following implementations of the algorithms for adding, multiplying, and transposing n X n matrices: for (i = 0; i < n; i++) for (j = 0;j < n; j++) a[i] [j] %3! b[i] [j] + c[i] [j]; %3D for (i = 0; i < n; i++) for (j = 0; j < n; j++) for (k = a[i] [j] = 0; k < n; k++) a[i] [j] += b[i] [k] * c[k] [jl; %3! %3D for (i = 0; i

Another recursive algorithm is applied to some data A = (a₁, ..., am) where m = 2* (i.e. 2, 4, 8,16 ...) where x is an integer ≥ 1. The running time T is characterised using the following recurrence equations: T(1) = c when the size of A is 1 T(m) = 2T (2) + c otherwise Determine the running time complexity of this algorithm.

The size of AxB, multiplication of two matrices A (with size mxp) and B(with size pxn) is

The Euclidean Algorithm can be used to find the highest common divisor. Can you please explain with examples what the Extended Euclidean Algorithm is and how to use it.