Question

Solve the system of equations x_1−3x_2+4x_3=-4 3x_1−7x_2+7x3=-8 −4x_1+6x_2−x_3=7

Forms of linear equations
ANSWERED
asked 2020-10-25
Solve the system of equations \(x_1−3x_2+4x_3=-4\)
\(3x_1−7x_2+7x3=-8\)
\(−4x_1+6x_2−x_3=7\)

Answers (1)

2020-10-26

Given:
\(x_1−3x_2+4x_3=-4\)
\(3x_1−7x_2+7x3=-8\)
\(−4x_1+6x_2−x_3=7\)
Step 1
Find the value of \(\delta_1\) & \(\delta_2\)
\(\delta_1=[[-4,-3,4],[3,-7,7],[-4,6,-1]]\)
=1(7-42)+3(-3+28)+4(18-28)
=-35+75-40
=0
Step 3
\(\delta_1=[[-4,-3,4],[-8,-7,7],[7,6,-1]\)
=-4(7-42)+3(8-49)+(-48+49)
=140-123
\(=21\ne0\)
according to cramers rule if value of is zero and if any one of \(/_\ 1, /_\ 2 or /_\ 3\) is non zero then the system of linear equations has no solution.
therefore the given system of linear equations has no solution

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