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Find the determinant of a matrix B when A is a 4x4 matrix with a neg. determinant (Linear Algebra)?
I am looking for hints to help me solve this problem. Thanks.
Let A be a 4x4 orthogonal matrix whose determinant is negative. What is the value of |B|, where B = (2*adj(A))^(-1)?
2 Answers
- The PrinceLv 61 decade agoFavorite Answer
If A is an orthogonal matrix with a negative determinant then its determinant must be negative one because orthogonal matrices always have a determinant of one or negative one. Since you are multiplying a 4x4 matrix with 2, the determinant is multiplied by 2^4=16 so the determinant is now -16. And then you take the matrix's inverse which means that you take the inverse of the determinant also. So the determinant of B is -1/16.
- 1 decade ago
I'm rusty but I think the answer is in the question itself... take a carefull look and see what you can do. or rather what you cant do.
