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Easy matrix/determinants question

by astonmartin
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Feb11-09, 08:52 PM
P: 23
1. The problem statement, all variables and given/known data

Suppose A and B are 3 x 3 matrices and det A = x ≠ 0 while det B = y. Let
C be the matrix ((2A)^-1 )B <-- (2A) inverse x B

then det C is:

2. Relevant equations

3. The attempt at a solution

det(2A) = 2x, so det 2A inverse = 1/(2x)
det C = y/(2x)...which is not one of the solutions

a) y/8x b) 2xy c) -2y/x d) 2y/x e) 8y/x

what am I missing here?
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Feb11-09, 09:19 PM
P: 26
You are very close; however,

[tex]\det(\alpha A)=\alpha^{n} \det(A)[/tex]

where n is the order of the matrix A, in this case 3. To understand why this happens, think of the determinant of the identity and multiply it by a scalar.

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