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JEE Main 202125 FebruaryEvening Shift
Exam
JEE Main
Year
2021
Date
25 February
Shift
Evening Shift
Subject
Mathematics
Chapter
Determinants

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

The following system of linear equations 2x + 3y + 2z = 9 3x + 2y +...

The following system of linear equations
2x+3y+2z=92x + 3y + 2z = 9
3x+2y+2z=93x + 2y + 2z = 9
x−y+4z=8x - y + 4z = 8

Options

  1. Ahas infinitely many solutions
  2. Bhas a unique solution
  3. Chas a solution (α,β,γ)\left(\alpha, \beta, \gamma\right) satisfying α+β2+γ3=12\alpha + {\beta}^{2} + {\gamma}^{3} = 12
  4. Ddoes not have any solution

Correct answer

B. has a unique solution

Step-by-step solution

2x+3y+2z=9...(1)</p><p>2x + 3y + 2z = 9 . . . \left(1\right)</p><p>3x + 2y + 2z = 9 . . . \left(2\right)</p><p></p><p>x - y + 4z = 8 . . . \left(3\right)

\left(1\right) - \left(2\right) ⇒ - x + y = 0 ⇒ x - y = 0</p><p>from(3)</p><p>from \left(3\right)4z = 8 ⇒ z = 2</p><p>from(1)2x+3y=5</p><p>from \left(1\right)2x + 3y = 5

⇒x=y=1⇒ x = y = 1

∴∴ system has unique solution.

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