Invertible Square Matrices and Determinants - Concept

Concept Concept (1)

In order to determine if a matrix is an invertible square matrix, or a square matrix with an inverse, we can use determinants. The only matrix with a nonzero determinant is an invertible square matrix. An invertible square matrix represents a system of equations with a regular solution, and a non-invertible square matrix can represent a system of equations with no or infinite solutions.

Sample Sample Problems (2)

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Invertible Square Matrices and Determinants - Problem 1
Problem 1
How to show that a 3x3 matrix, [3 3 4; 4 4 6; 1 1 2], is not invertible by computing its determinant.
Invertible Square Matrices and Determinants - Problem 2
Problem 2
How to show that a 3x3 matrix, [2 5 3; -15 10 18; 20 50 30], is not invertible by computing its determinant.