Mathegoras

Vectors and matrices › Matrices › Inverses and singular matrices

Smallest entry sum for a conjugating matrix

High school · ●●●○○ 50 pts

For some matrix P=(abcd)\mathbf{P} = \begin{pmatrix} a & b \\ c & d \end{pmatrix} with nonzero integer entries, (43−10)=P−1(1003)P\begin{pmatrix} 4 & 3 \\ -1 & 0 \end{pmatrix} = \mathbf{P}^{-1} \begin{pmatrix} 1 & 0 \\ 0 & 3 \end{pmatrix} \mathbf{P}. Find the smallest possible value of ∣a∣+∣b∣+∣c∣+∣d∣|a| + |b| + |c| + |d|.

Sign in to save your progress.

integer optimization