Problem #2: (a) Find the determinant of the following matrix. A = B = 2 2 1 (b) Find the determinant of the following matrix. Problem #2(a): Problem #2(b): 030O 3 -1 2 2 -2 WAŃ W W 2 0 0 -3 -1 2 2 0 -2 3 0 0 -4 4 4 Hint: Do a row operation first. 0 0 0 0 0 0 2 0 2 -2 II

The sum of the digits of a four-digit number is 23. The ones digit is 4 times the thousands digit. If you add the tens and thousands digit the sum is 6 more than the ones digit. If the digits are reversed in order, the new number is 2997 more than the original number. Find the original four-digit number. (a) What are the equations? (b) What is the determinant of the coefficient matrix? (c) Find the four-digit number using the Gauss-Elimination (d) Find the four- digit number using the LU-decomposition

Problem 2. Use row operations to compute the determinant, 0 4 0 -4 1 3 -2 -4 3 2 0 (a) (b) 0 0 3 1 2 0 0 0 2 3 -2 1 2-1 1

G2. Show how to compute the determinant of the matrix -4 -1 6 -1 -2 2 A = 6 5 -1 -1 -5 -3