The Determinant of a 3x3 Matrix calculator compute the determinant of a 3x3 matrix.
INSTRUCTIONS: Enter the following:
Determinant (det): The calculator returns the determinate as a real number.
The Determinant of a 3x3 calculator computes the determinant of a 3x3 matrix, a useful mathematical construct derived from a square matrix:
A = `|[A_11,A_12,A_13],[A_21,A_22,A_23],[A_31,A_32,A_33]|`
The determinant can be used for a number of linear algebra applications like solving a set of linear equations and determining the characteristic polynomial of a matrix in computing eigenvalues.
Inputs to the matrix above are nine numeric values, where the cells of the matrix are ordered as:
A11, A12, A13
A21, A22, A23
A31, A32, A33
Output for the formula is the determinant of matrix A, illustrated by the following graphic:
The picture above shows the order of the multiplications to obtain six terms which are then added together to compute the determinant. The picture gives you a visual pattern to employ when computing a determinant.
Note that four of the six diagonals intersect a term which has to be brought over to complete the diagonal. Another way to think about it visually, is that the diagonal for Term 3, which starts with `A_12` wraps around the matrix to hit `A_31`.
To compute the first term you multiply the terms on the red diagonal: Term 1 = `A_11 * A_22 * A_33`
Let's look at how the six terms are obtained.
Each of six terms then compute like:
det(A) = (Term 1 - Term2) + (Term 3 - Term 4) + (Term 5 - Term 6)