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`det = |A|`

Enter a value for all fields

The **Determinant of a 3x3 Matrix** calculator compute the determinant of a 3x3 matrix.

**INSTRUCTIONS**: Enter the following:

- (
**A**) 3x3 Matrix

**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:

A_{11}, A_{12}, A_{13}

A_{21}, A_{22}, A_{23}

A_{31}, A_{32}, A_{33}

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:

**Term 1 = `A_11 * A_22 * A_33`****Term 2 = `A_11 * A_23 * A_32`****Term 3 = `A_12 * A_23 * A_31`****Term 4 = `A_12 * A_21 * A_33`****Term 5 = `A_13 * A_21 * A_32`****Term 6 = `A_13 * A_22 * A_31`**

det(A) = (**Term 1** - **Term2**) + (**Term 3** - **Term 4**) + (**Term 5 **- **Term 6**)

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