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Problem 2: Matrix Vector Operations [5pt] a) Create a program named my_dot Product which USING LOOPS calculates the dot prod- uct of two vectors (of dimensions 1 x n) from the keyboard. The program should check the input from the user making sure that the vectors are the right dimensions. If the vectors are not then an error message should be outputted to the user. If the vectors are of the right dimensions then the answer should be outputted to the user. Using your code, complete the following table: 31-2j+4k 2i+2j-3k 0i+Oj-1k1i-Oj+Ok 21+13+2k -li+2j+5k b) Create a program named my_arrayCount which inputs an n xm array and determines (USING LOOPS) how many elements in the array are greater than zero and how many are less than zero. The program should then output the answers. Using your code, complete the following table: n (>0) n (