[Solved] Why does the determinant of a matrix become zero when two rows of the matrix are identical? — Ans: Because the matrix is singular and rows are linearly dependent. | MATLAB

MATLAB - Linear Algebra

Why does the determinant of a matrix become zero when two rows of the matrix are identical?

ABecause the matrix is singular and rows are linearly dependent.

BBecause the matrix is symmetric.

CBecause the matrix is diagonal.

DBecause the matrix has only positive elements.

Step-by-Step Solution

Solution:

Step 1: Understand linear dependence and singularity
If two rows are identical, they are linearly dependent, meaning one row can be formed by the other.
Step 2: Connect linear dependence to determinant value
Linear dependence causes the matrix to be singular, which means its determinant is zero.
Final Answer:
Because the matrix is singular and rows are linearly dependent. -> Option A
Quick Check:
Identical rows imply zero determinant [OK]

Quick Trick: Identical rows make determinant zero [OK]

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