Let J be the n ( n matrix of all 1's and consider A = (a -
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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)?
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bba b b a b abb b
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a Doing the given operations does not change the determent of A since the given operations are al...View the full answer
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