EBK PRECALCULUS W/LIMITS
3rd Edition
ISBN: 9781285607160
Author: Larson
Publisher: CENGAGE CO
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Question
Chapter 8.5, Problem 16E
To determine
To solve: system of linear equations using Cramer’s rule
{5x−4y+z=−14−x+2y−2z=103x+y+z=1
Expert Solution & Answer
Answer to Problem 16E
(x,y,z)=(0,3,−2)
Explanation of Solution
First find the coefficient matrix of this system,
A=[5−41−12−2311]
Determinant of the coefficient matrix A is:
D=|5−41−12−2311|=5|2−211|−(−4)|−1−231|+1|−1231|=5(2+2)+4(−1+6)+1(−1−6)
=20+20−7=33
Since D≠0 , Cramer’s rule can be applied.
Consider,
Dx=|−14−41102−2111|=−14|2−211|−(−4)|10−211|+1|10211|=14(2+2)+4(10+2)+1(10−2)
=−56+48+8=0
Dy=|5−141−110−2311|=5|10−211|−(−14)|−1−231|+1|−11031|=5(20+2)+14(−1+6)+1(−1−30)
=60+70−31=99
Dz=|5−4−14−1210311|=5|21011|−(−4)|−11031|+(−14)|−1231|=5(2−10)+4(−1−30)−14(−1−6)
=−40−124+98=−66
Now determine x ,
x=DxD=033=0
Now determine y ,
y=DyD=9933=3
Now determine z ,
z=DzD=−6633=−2
So, the solution of the given system is,
(x,y,z)=(0,3,−2)
Chapter 8 Solutions
EBK PRECALCULUS W/LIMITS
Ch. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - Prob. 4ECh. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10E
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