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Cramer's Rule 3X3 System

This video explains how to solve a 3x3 system of linear equations using Cramer's Rule (0:05). Here I demonstrated the method where I calculated the main determinant (D) and the determinants for each variable (DX, DY, DZ) (0:36). Key Steps for Cramer's Rule: 1. Calculate D: Find the determinant of the coefficient matrix (0:38). 2. Calculate DX, DY, DZ: Replace the respective column of the coefficient matrix with the constant matrix to find the specific determinants (4:07). 3. Find Variables: Solve for x, y, and z by dividing the variable determinant by the main determinant (e.g., x = DX / D) (13:06). Results for the example problem: D = 46 (4:02) DX = -46 (7:03) DY = 92 (9:28) DZ = 46 (11:52) Final Solutions: x = -1 (13:28) y = 2 (13:53) z = 1 (14:02) TIMESTAMPS [00:00:00] Introduction and Equations setup [00:00:34] Setting up the first determinant (D) [00:00:56] Step-by-step determinant expansion method [00:03:59] Final calculation for the value of D [00:04:09] Calculating the determinant for X (Dx) [00:07:07] Calculating the determinant for Y (Dy) [00:09:34] Calculating the determinant for Z (Dz) [00:11:50] Summary of the calculation patterns [00:13:08] Solving for the variables x, y, and z [00:14:04] Final summary and conclusion