# Determinant problem

• Jan 13th 2008, 11:15 AM
Determinant problem
A = [ a b . . . b ]
[ b b . . . b ]
[ b b . . . a ]

What is the determinant of A?
What conditions would allow det A not equal to 0?

det A = 2a (ba - b^2) or 0, since the middle terms would all be eliminated.

det A not equal to 0 when a not equal to 0, with the number of row + number of columns = even.
• Jan 13th 2008, 05:59 PM
mr fantastic
Quote:

A = [ a b . . . b ]
[ b b . . . b ]
[ b b . . . a ]

What is the determinant of A? Mr F says: Are you suggesting that the order of the matrix is 3xm where m > 3. If so, the determinant does not exist.

What conditions would allow det A not equal to 0?

det A = 2a (ba - b^2) or 0, since the middle terms would all be eliminated.

det A not equal to 0 when a not equal to 0, with the number of row + number of columns = even.

Or do you mean $A = \left( \begin{array}{ccc}
a & b & b \\
b & b & b \\
b & b & a \\ \end{array} \right) \,$
? In which case, $\det(A) = b(a - b)^2 = 0$ when $a = b$ or $b = 0$.