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GATE 2026 IN – Question 14

Engineering Mathematics · Linear algebra and matrices · 1 mark · Multiple choice

Consider the matrix $$A=\begin{bmatrix}1&0&2\\-1&1&0\\0&1&2\end{bmatrix}.$$

Let $$b=\begin{bmatrix}1\\3\\0\end{bmatrix},\qquad x=\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}.$$

The number of solutions to the linear system $Ax=b$ is ________.

  1. 0
  2. 1
  3. 6
  4. Infinitely many

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Show answer and explanation

Correct answer: (A) 0

Explanation

The equations are $x_1+2x_3=1$, $-x_1+x_2=3$, and $x_2+2x_3=0$. Adding the first two requires $x_2+2x_3=4$, contradicting the third equation.

The system is inconsistent and has **0 solutions (A)**.