Find the determinant of the resulting matrix from b.

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Reference no: EM131073923

Apply the result of Exercise 16 to find the determinants of the following matrices, and confirm your answers using a matrix program.

Exercise 16

Let J be the n X n matrix of all 1's, and consider A = (a - b) I + bJ ; that is,

Confirm that det A = (a - b)n-1 [a + (n - 1)b] as follows:

a. Subtract row 2 from row 1, row 3 from row 2, and so on, and explain why this does not change the determinant of the matrix.

b. With the resulting matrix from part (a), add column 1 to column 2, then add this new column 2 to column 3, and so on, and explain why this does not change the determinant.

c. Find the determinant of the resulting matrix from (b).

Reference no: EM131073923

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