Question

If the points \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) are collinear, then the rank of the matrix \[ \begin{bmatrix} x_1 & y_1 & 1
x_2 & y_2 & 1
x_3 & y_3 & 1 \end{bmatrix} \]

• A. Will always be less than 3
• B. 2
• C. 1
• D. None of these

Hint:

When points are collinear, the matrix formed by the coordinates of these points will have a rank of 2.

Answer 1

The Correct Option is B

Step 1: Understanding collinearity.
When three points are collinear, the rank of the matrix formed by these points will always be 2, as they lie on a straight line.

Step 2: Conclusion.
The correct rank is 2, corresponding to option (2).