Let J be the n ( n matrix of all 1's and consider
A = (a - b)I + b J ; 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)?

Transcribed Image Text:

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