Programming option: All programs must compile. Each program may be submitted only once. Late programs will not be accepted. Programs should give the user clear instructions. I/O formats should be easy to read and well organized. Program code must be well documented. Programs are to be submitted via e-mail to msulliva@math.siu.edu with the subject line "221: program #n, your name". You can use C, C++, Basic, FORTRAN or Pascal. Indicate which in your beginning comments. You may not collaborate on program assignments! 1) Due with Hwk Set 2. Points: 5 The user will enter two matrices. The program will multiply the two matrices. The program should give an error message if the sizes of the matrices do not allow them to be multiplied. 2) Due with Hwk Set 3. Points: 5 The user will enter a 4x4 matrix. Write a program that finds the inverse. The program should give an error message if the matrix is singular. 3) Due with Hwk Set 5. Points: 10 The user will enter a square matrix (of any size). The program finds the determinant. 4) Due with Hwk Set 6. Points: 5 The user is to enter three points in R^3. If the three points do not determine a unique plane the program is to give an appropriate error message. Otherwise the program finds the equation of the unique plane containing these three points and outputs the equation in the form Ax + By + Cz = D. 5) Due with Hwk Set 8. Points: 5 Write a program for the Gram-Schmidt process. 6) Due with Hwk Set 9. Points: 10 Write a program to do QR factorization. 7) Due with Hwk Set 11. Points: 10 Write a program of your own.