Ayn Generes

arg5970
Week 11

Problem 7.1.4
URL: http://people.tamu.edu/~arg5970/311_7.1.4.html  

PROBLEM:

Consider:

 

  1. Guess the answer by analogy with the previous exercise (set x1=1, x2=2,x3=3,x4=4)
  2. Calculate the determinant by the row-reduction method.

SOLUTION:

a.

=(x2-x1)(x3-x1)(x3-x2)(x4-x3)(x4-x2)(x4-x1)

=(2-1)(3-1)(3-2)(4-3)(4-2)(4-1) = 12

b.

[(2) x -3 ] + (3)

[(2) x -7] + (4)

 [(3) x -6] + (4)      
         

Now that it is a triangular matrix, multiply the diagnols to get the determinant.

= (1)(1)(2)(6) = 12

As shown, answer is obtained by the first method and row-reduction.