Evaluate Determinants & Apply Cramer’s Rule

Determinant of a 3X3 Matrix 1 2 3 2 −1 −3 4 1 0 3 −4 −2 2 −1 4 1 3 −4 4 5 6 + + 2∙1∙−2 −1∙0∙3 −3∙4∙−4 - + + (3∙1∙−3 −4∙0∙2 −2∙4∙−1) ) - =−4+0+48 (−9+0+8) =44−(-1) =44+1=45

Cramer’s Rule for a 2X2 System Use Cramer’s rule to solve this system 9x + 4y = -6 3x – 5y = -21 x = 𝑏𝑎𝑐𝑘 𝑦 𝑐𝑜𝑙𝑢𝑚𝑛 𝑐𝑜𝑙𝑢𝑚𝑛 𝑥 𝑦 𝑐𝑜𝑙𝑢𝑚𝑛 𝑐𝑜𝑙𝑢𝑚𝑛 = −6 4 −21 −5 9 4 3 −5 = 30−(−84) −45−12 = 114 −57 x = -2 y = 𝑥 𝑏𝑎𝑐𝑘 𝑐𝑜𝑙𝑢𝑚𝑛 𝑐𝑜𝑙𝑢𝑚𝑛 𝑥 𝑦 𝑐𝑜𝑙𝑢𝑚𝑛 𝑐𝑜𝑙𝑢𝑚𝑛 = 9 −6 3 −21 9 4 3 −5 = −189−(−18) −45−12 = −171 −57 y = 3