The following system of linear... | Linear Algebra JEE Main 2021

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JEE MAIN 2021

25-02-2021 S2

Question

The following system of linear equations 2x + 3y + 2z = 9 3x + 2y + 2z = 9 x – y + 4z = 8

Select the correct option:

has a solution $(\alpha, \beta, \gamma)$ satisfying $\alpha+\beta^2+\gamma^3=12$

has infinitely many solutions

does not have any solution

has a unique solution

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

2x + 3y + 2z = 9 ...(1) 3x + 2y + 2z = 9 ...(2) x – y + 4z = 8 ...(3) (1) – (2) ⇒ –x + y = 0 ⇒ x – y = 0 from (3) 4z = 8 ⇒ z = 2 from (1) 2x + 3y = 5 ⇒ x = y = 1 ∴ system has unique solution

Question Tags

JEE Main

Mathematics

Easy

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