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GATE 2026 CE (CE1) – Question 12

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Multiple choice

Given:

$$\begin{bmatrix} 1 & 1 & 1 \\ 1 & 0 & 2 \end{bmatrix}\begin{Bmatrix} x_1 \\ x_2 \\ x_3 \end{Bmatrix} = \begin{Bmatrix} 0 \\ 0 \end{Bmatrix}$$

The above system of equations represents a

  1. plane
  2. line
  3. volume
  4. point

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Show answer and explanation

Correct answer: (B) line

Explanation

Each equation is a plane in three dimensions, and the two planes are not parallel, so they meet along a line. The solution has one free parameter: $x_1 = -2x_3$ and $x_2 = x_3$.