(a) For the triangle in the accompanying figure, use trigonometry to show that and then apply Cramer's rule to show that (b) Use Cramer's rule to obtain similar formulas for and . Figure Ex-29
M303 Section 3.2 Notes- Properties of Determinants 10-19-16 Key to “efficient” computing of determinants is understanding how row operations affect them Theorem 3- Let be × : o If obtained from by row replacement, then det = det o If obtained by row swapping, then det = −det 1 o If obtained by nonzero scaling, then det = det →det = det − − − Ex. |5 2 3| − − − − − − 2→ = 2 | 5 2 3 | − − − Think of like factoring out 2 −8 6 8 Ex. Compute det = |3 −9 5 10 |using row reduction. −3 0 1 −2 1 −4 0 6 1 −4 3 4 1 3 −9 5 10 1→ 2=12| −3 0 1 −2 | 1 −4 0 6 1 −4 3 4 2 −23 1 0 3 −4 −2 { 3 +33 =12 | | 4→ 4 1 0 −12 10 10 0 0 −3 2 1 −4 3 4 → + 4 = 2| 0 3 −4 −2 | 3 3 2 0 0 −6 2 0 0 −3 2
