1. Evaluate Determinants & Apply Cramer’s Rule

2. Determinant of a 3X3 Matrix1 2 3
2 −1 − −4 −2
2 − −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

3. 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
= 30−(−84) −45−12
= 114 −57
x = -2
y = 𝑥 𝑏𝑎𝑐𝑘 𝑐𝑜𝑙𝑢𝑚𝑛 𝑐𝑜𝑙𝑢𝑚𝑛 𝑥 𝑦 𝑐𝑜𝑙𝑢𝑚𝑛 𝑐𝑜𝑙𝑢𝑚𝑛
= 9 −6 3 − −5
= −189−(−18) −45−12
= −171 −57
y = 3