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

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