What is a determinant?
A determinant is a scalar value that helps describe a matrix and can be used to determine whether a matrix is invertible or singular.
For a 2×2 matrix [[a,b],[c,d]], det = ad − bc
For a 3×3 matrix, use expansion by minors or a diagonal rule to compute the determinant.
Example
Given [[4,2],[1,3]], the determinant is 4×3 − 2×1 = 10.
Frequently Asked Questions
Why is determinant useful?
It helps in solving systems of equations, checking invertibility, and understanding geometric transformations.
What if the determinant is zero?
A zero determinant means the matrix is singular, so it does not have an inverse.
Can I use this for 3×3 matrices?
Yes. The calculator supports 2×2 and 3×3 matrix inputs so you can compute determinant values for more advanced problems.