For the system of linear equations which of the following is NOT correct?

It has infinitely many solutions if Explanation: Given system of eqn can be written as and Now, for unique solution and and for infinite solutions and

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

For the system of linear equations

2x + 4y + 2az = b

x + 2y + 3z = 4

2x - 5y + 2z = 8

which of the following is NOT correct?

Choose the correct answer:

Explanation

Given system of eqn can be written as

[A : B] = \begin{bmatrix} 1 & 2 & 3 & : & 4 \\ 2 & -5 & 2 & : & 8 \\ 2 & 4 & 2a & : & b \end{bmatrix}

$R_2 \to R_2 - 2R_1$ and $R_3 \to R_3 - 2R_1$

\Rightarrow [A : B] \sim \begin{bmatrix} 1 & 2 & 3 & : & 4 \\ 0 & -9 & -4 & : & 0 \\ 0 & 0 & 2a - 6 & : & b - 8 \end{bmatrix}

Now, for unique solution $2a - 6 \neq 0$ and $b - 8 \in \mathbb{R}$

\Rightarrow a \neq 3 \text{ and } b \in \mathbb{R}

and for infinite solutions $2a - 6 = 0$ and $b - 8 = 0$

\Rightarrow a = 3 \text{ and } b = 8

Choose the correct answer:

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