Math Problem Statement
Let A be a 2 * 2 matrix with integer such that:
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A ^ 2 = 3A
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det(A) = 6
Consider the matrix A reduced modulo 7. Determine how many distinct values the trace of the resulting matrix can take
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Theory
Eigenvalues and Eigenvectors
Modular Arithmetic
Formulas
A^2 = 3A
det(A) = ad - bc
Trace of A = a + d
Theorems
Cayley-Hamilton Theorem
Eigenvalue Determinant Theorem
Suitable Grade Level
Undergraduate Level
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