Register to reply 
Easy matrix/determinants questionby astonmartin
Tags: None 
Share this thread: 
#1
Feb1109, 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? 


#2
Feb1109, 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. 


Register to reply 
Related Discussions  
Trace of a matrix equals sum of its determinants?  Linear & Abstract Algebra  2  
Linear Algebra  invertible matrix; determinants  Calculus & Beyond Homework  2  
Determinants of a matrix  Precalculus Mathematics Homework  7  
Determinants 4x4 matrix  Precalculus Mathematics Homework  2  
Determinants and Matrix Inverses Proofs  Linear & Abstract Algebra  6 