Answer questions 10, 21

ADDING INTEGERS Mathematical folklore has it that Gauss discovered the formula 1+2+3+..+n = n(n+ 1)/2 when he was only ten years old. To occupy time, his teacher asked the students to add the integers from 1 to 100. Gauss immediately wrote an answer and turned his slate over. To his teacher's amazement, Gauss had the only correct answer in the class. Young Gauss had recognized that the numbers could be put in 50 sets of pairs such that the sum of each pair was 101: (50 + 51) + (49 + 52) + (48 +53) + ... + (1 + 100) = 50(101) = 5050. Soon his brilliance was brought to the attention of the Duke of Brunswick, who thereafter sponsored the education of Gauss. 4.2 EXERCISES Consider the matrices in Exercises 1-10. 12. a) Either state that the matrix is in echelon form 00 2 or use elementary row operations to transform it to echelon form. 13. 14. 1 2 2 1 b) If the matrix is in echelon form, transform it 3 0 10 0 to reduced echelon form. 15. 16. 2 0 O 17. 18. 2 19. 2 20. 0 2 -2 -2 - 21. 10. In Exercises 22-35, solve the system by transforming the augmented matrix to reduced echelon form. In Exercises 11-21, each of the given matrices represents 22. 2x1 - 3.12 - the augmented matrix for a system of linear equations. 4x + 613 - -10 In each exercise, display the solution set or state that the 23. X1 - 212 - 3 system is inconsistent. 2x1 - 453 - 1