Please ans all the ques in Java language

Homework-4: Due on November 21t, 2018 in dass 1. The transpose of a matrik A, denoted by AT is defined as a matrix obtained by interchanging its rows and columns. For example: A [ 2 9 10 11 12 26 10 3 7 11 4812 Write a program that asks for the dimensions of a matrix (nRows, nCols) from the console and then creates the matrix with random numbers. Then it finds the transpose of the matrix and displays the original matrix and the transpose on the console. 2. A square matrix A is said to be symmetric ifAT A, e. if its transpose is identical to the matrix itself. Write a program that creates a square matrix of dimension NX N. The value of N should be provided by the user. Then it checks if the matrix is symmetric and displays a message accordingly (i.e., Symmetric or Not Symmetric). Test your program with two example matrices which are respectively symmetric and not symmetric. You have used the toUpperCase) and tolowerCasel) methods of the String class. Write your own routines MyUpperCase) and MylowerCase) that would accept a String as input and then would convert it respectively to uppercase and to lowercase. Display the original string, the converted string in uppercase and the converted string in lowercase. 3. Write a program that accepts a sentence from a user and then counts the number of occurrences of each letter from 'a to z', ignoring the case. If a letter does not appear in the sentence, the program should not display its count as O. It should only display the counts of the letters which appeared in the text 4. Write a program that initializes a square matrix Mat of dimension N x N, where the value of N is provided by the user from console. it then creates a 1 dimensional array A with the non-diagonal elements of the matrix. The elements should be read from the matrix in column-major order. The program should display both the original matrix Mat and the array A (The length of the array A should be N -N). 5