Determinants

Determinant of a 2x2 Matrix

Compute the determinant of a 2x2 matrix A using the formula det(A) = ad - bc. The two diagonal products are computed first, then subtracted. The state panel tracks each product and the final result.

Example

Compute the two diagonal products and subtract.

highlighted = computed this step

Step 1 — Set up

Start with the given matrix data.

A=[3214]A=\begin{bmatrix}3&2\\1&4\end{bmatrix}

Step 2 — Main diagonal product

a·d = 3*4 = 12.

a⋅d=3⋅4=12a\cdot d=3\cdot 4=\hl{12}

Step 3 — Other diagonal product

b·c = 2*1 = 2.

b⋅c=2⋅1=2b\cdot c=2\cdot 1=\hl{2}

Step 4 — Result

det = ad - bc = 12 - 2 = 10.

det⁡(A)=12−2=10\det(A)=12 - 2=\hl{10}
determinant formula (2x2) For A = [[a,b],[c,d]], det(A) = a*d - b*c. The two terms correspond to the main diagonal product and the anti-diagonal product.