Register to reply

Easy matrix/determinants question

by astonmartin
Tags: None
Share this thread:
astonmartin
#1
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?
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
shaggymoods
#2
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.


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