Write and test a Python function, that makes use of numpy, to return the sum of the elements on the main diagonal (upper left to lower right) of a square matrix. In linear algebra, this value is called the trace of the matrix. For example, with a matrix represented as a list of lists eg. [[9, 8, 7], [6, 5, 4], [3, 2, 1]], your function should return (9 + 5 + 1) = “15” Your Python function solution should work for any sized square matrix passed to it. Demonstrate that this is the case with 3x3, 4x4, and 6x6 matrix examples.

e) The power to a motor in a group conveyor system is controlled by the state of Four Sensor Switches A,B,C and D. The motor is to be switched on when:- All sensor switches are OPEN- Any one switch is CLOSED and the remaining three OPEN- B and C CLOSED, A and D OPEN- A and D CLOSED, B and C OPEN Assuming Switch closed = logic 1 and Switch open =0 Design the logic circuit to control the motor using NOR gates only [5 marks]

You are given an array-like data structure Listy which lacks a size method. It does, however, have an elementAt ( i) method that returns the element at index i in 0( 1) time. If i is beyond the bounds of the data structure, it returns -1. (For this reason, the data structure only supports positive integers.) Given a Listy which contains sorted, positive integers, find the index at which an element x occurs. If x occurs multiple times, you may return any index.  Write code with explanation

Implement a function countMultiples in Python that: accepts a single argument, a 2-dimensional list (e.g, list of lists) containing non-negative integers, and returns the count of those integers that are multiples of 5 but that are not not multiples of 10. (e.g., 65 should be counted, but 80 should not be counted) sample usage: >>> countMultiples( [[1,2,3],[4,5],[6,7,8,9]] ) # 5 counts1

Create a function that takes the dimensions of two triangles (as arrays) and checks if the first triangle fits into the second one. Examples does TriangleFit([1, does TriangleFit([1, does TriangleFit([1, does TriangleFit([1, 1, 1], [1, 1, 1]) → true 1, 1], [2, 2, 2]) → true 2, 3], [1, 2, 2]) → false 2, 4], [1, 2, 6]) → false

Implement the following function that returns a vector of vectors of Item, each of which is a subset of elements chosen from the given vector a[first…last]:  /* if a is {1,2,3}, first=0, last=2, the function shall returns a vector of the following vectors:    {}, {1}, {2}, {3}, {1,2},{1,3}, {2,3},{1,2,3}, all subsets of a[0…2].    Precondition: last-first+1>=1, i.e., there is at least one element in the a[first…last]    Note 1)if the length of a[first…last] is n, then the function should return a vector of 2n vectors      2) The order of these subsets does not need to match what’s listed here…  */ vector<vector<int>> subsets (const vector<int> & a, int first, int last)   code

Create a function append(v, a, n) that adds to the end of vector v a copy of all the elements of array a. For example, if v contains 1,2, 3, and a contains 4, 5, 6, then v will end up containing 1, 2, 3, 4, 5,6. The argument n is the size of the array. The argument v is a vector ofintegers and a is an array of integers. Write a test driver.

Implement a function findMixedCase in Python that: accepts a single argument, a list of words, and returns the index of the first mixed case word in the list, if one exists, (a word is mixed case if it contains both upper and lower case letters), and returns -1 if the all words are either upper or lower case. sample: >> findMixedCase( ['Hello','how','are','you'] ) # 'Hello' is mixed case0