8.8. Cramer’s Rule http://www.ck12.org
x=∣∣
∣∣^7212
108 − 12
∣∣
∣∣
∣∣
∣∣^512
18 − 12
∣∣
∣∣
=^725 ··((−−^1212 ))−− 1212 ··^10818 =− 2762160 =^18023
y=∣∣
∣∣^572
18 108
∣∣
∣∣
∣∣
∣∣^512
18 − 12
∣∣
∣∣
=^5 ·^108276 −^72 ·^18 =− 276756 =−^6323
- Input the following three matrices into your calculator. MatrixAhas columns that are the constants and they
coefficients. MatrixBhas columns that arexcoefficients and the constants. MatrixCis just the coefficient matrix.
A=
[− 112 21
15 − 21
]
B=
[ 70 − 112
27 15
]
C=
[ 70 21
27 − 21
]
Then computex=detdetCAandy=detdetCB
The solution isx=− 1 ,y=− 2
3.
3 x+ 2 y+z= 7
4 x+ 0 y+z= 6
6 x−y+ 0 z= 5z=∣∣
∣∣
∣∣
3 2 7
4 0 6
6 −1 5
∣∣
∣∣
∣∣
∣∣
∣∣
∣∣
3 2 1
4 0 1
6 −1 0
∣∣
∣∣
∣∣
=^0 + 02 +· 26 ·· 16 +· 67 +· 14 ··( 4 −·(^1 −) 1 −)^0 −− 0 (−−(^1 −) 1 ·^6 )·· 13 −· 35 −·^40 ·^2 =^2211 = 2
Practice
Solve the following systems of equations using Cramer’s Rule. If one solution does not exist, explain.