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JEE Main 202125 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
25 February
Shift
Morning Shift
Subject
Mathematics
Chapter
Determinants

JEE Main 2021 · 25 February · Morning Shift · Mathematics · Determinants

If the system of equations kx + y + 2z = 1 3x - y - 2z = 2 - 2x -...

If the system of equations

kx+y+2z=1kx + y + 2z = 1

3x−y−2z=23x - y - 2z = 2

−2x−2y−4z=3- 2x - 2y - 4z = 3

has infinitely many solutions, then kk is equal to ______ .

Correct answer

0

Step-by-step solution

If the system of equations

P1:kx+y+2z=1{P}_{1}: kx + y + 2z = 1

P2:3x−y−2z=2{P}_{2}: 3x - y - 2z = 2

P3:−2x−2y−4z=3{P}_{3}: - 2x - 2y - 4z = 3

Which are equivalent to equations of planes.

We observe 5P2−P1=3P35{P}_{2} - {P}_{1} = 3{P}_{3}

So, 15−K=−615 - K = - 6

⇒K=21⇒ K = 21

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