STAT 200 Final: Untitled3

9. The rank of 3 2 1 4 7 0 90 2 5 6 0 | 12 7 16 4 ) Is (A) 1, (B) 2, (C)3, (D) 4.

Version 1 MATH 133 Final Exam - April 18, 2008 II.2 (15 points) Consider the matrix M = [1 1 | 1 2 1 2 3 5 | 1 3 4 5 5 14 6 -3 71 -5 8 -6 11 -13 23 -7 9 . (a) Find the reduced echelon form of M, showing your work. (You should find that M has rank 3.)

Your program will take an arithmetic expression as a String input. For Example:

• “1+2*(3/4)”

• “1+2*[3*3+{4–5(6(7/8/9)+10)–11+(12*8)]+14”

• “1+2*[3*3+{4–5(6(7/8/9)+10)}–11+(12*8)/{13+13}]+14”

Program

Your program will determine whether the open brackets (the square brackets, curly braces and the parentheses) are closed in the correct order.

Outputs:

Output 1

1+2*(3/4)

This expression is correct.

Output 2

1+2*[3*3+{4–5(6(7/8/9)+10)–11+(12*8)]+14

This expression is NOT correct.

Error at character # 10. ‘{‘- not closed.

Output 3

1+2*[3*3+{4–5(6(7/8/9)+10)}–11+(12*8)/{13+13}]+14

This expression is correct.

Output 4

1+2]*[3*3+{4–5(6(7/8/9)+10)–11+(12*8)]+14

This expression is NOT correct.

Error at character # 4. ‘]‘- not opened.

Task 1

Solve the above problem using an array-based stack.

Task 2

Solve the above problem using a linked list-based stack.