First Principles AI

Accedmychevron_right11thchevron_rightmathchevron_rightMatrices And Determinantschevron_rightExercise 4.3

Key idea

For a square system $AX=B$ with $|A|\ne 0$ , Cramer’s rule gives:

x_i=\frac{|A_i|}{|A|}

where $A_i$ is obtained from $A$ by replacing the $i$ -th column by $B$ .