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

Use the given inverse of the coefficient matrix to solve the following system. 7x₁ + 3x₂ = 12 - 6x₁-3x₂: = 4 A1 = -2 1 (Simplify your answers.) 3 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. x₁ = and x₂ = OB. There is no solution.

The answer is apparently -5, but when I reduced it to row echelon form I got 10. Also, am I only supposed to make the lower triangualr numbers zero when reducing to row echelon form?

Answer: Find the determinant of the following 2 x 2 matrix. -7] -6