Mathpapa counter advanced calculator.(Laplace expansion) Remember "What is the determinant of a 5x5 matrix"? The question from the previous section? Finally, we can touch on this topic and introduce a powerful tool to help us solve the determinant formula. Let A be a square matrix of size n. Suppose that the jth row (or column) of A has elements a₁,a₂,...,aₙ. Denote by Aᵢ to remove the entire matrix from A we have rows and columns of aᵢ (Aᵢ is a square matrix of size n-1). Then |A| = (-1)j+1 * a₁ * |A₁| + (-1)j+2 * a₂ * |A₂| + ...+ (-1)j+n * aₙ * |Aₙ |. If we've seen it, now it's a useful tool. And it's fun to use! For example, if they asked us how to find the determinant of a 3x3 matrix, we could grab a piece of paper and pick, say, the matrix's Third row, it will definitely take a long time to read through all this theory! If you want to learn more, visit our dedicated cofactor expansion calculator. We'll look at an example at the end.
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