What is the difference between singular and non-singular matrices?
My textbook says a matrix is singular if its determinant is zero. But why does that matter for solving linear equations? And how does this connect to the concept of inverse matrices?
1 Answer
DMDivya Mehta
✓ Accepted
· 13d ago
▲ 16
A singular matrix (det = 0) has no inverse, meaning the system Ax = b either has no solution or infinitely many solutions. A non-singular matrix (det != 0) has a unique inverse, and the system Ax = b has exactly one solution: x = A^(-1)b. Geometrically, a singular transformation collapses space into a lower dimension — you lose information and cannot uniquely recover input from output.
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