Matrix Solver, Determinant 2 by 2 Matrix

**2 by 2 matrix determinant** in this form
\[
\begin{pmatrix}
a \ \ \ b \\
c \ \ \ d
\end{pmatrix}
\]

The MathCrave 2 by 2 Matrix determinants calculator computes the determinant of a 2x2 matrix by multiplying the numbers on the main diagonal and subtracting the product of the numbers on the other diagonal.

MathCrave 2 by 2 Matrix determinants calculates the determinant of a 2x2 matrix by multiplying the values in the main diagonal (top-left to bottom-right) and subtracting the product of the other diagonal (top-right to bottom-left).

The determinant of a 2 by 2 matrix [A] is given by the formula:

**|A| = a*d - b*c**

where [A] = [[a, b], [c, d]] represents the given 2 by 2 matrix.

To solve for the determinant of a 2 by 2 matrix, follow these steps:

Step 1: Identify the matrix [A] = [[a, b], [c, d]].

Step 2: Apply the determinant formula: |A| = a*d - b*c.

Step 3: Substitute the respective values of a, b, c, and d into the formula.

Step 4: Perform the necessary arithmetic operations.

Step 5: The result obtained is the determinant of the given 2 by 2 matrix.

Example: Calculate the determinant of the matrix [B] = [[3, 2], [7, 5]].

Step 1: Identify the matrix

**[B] = [[3, 2], [7, 5]].**Step 2: Apply the determinant formula:

**|B| = a*d - b*c.**Step 3: Substitute the values of a, b, c, and d:

**|B| = (3*5) - (2*7).**Step 4: Perform the arithmetic operations:

**|B| = 15 - 14.**Step 5: The determinant of matrix B is

**|B| = 1.**Therefore, the determinant of the matrix

**[B] = [[3, 2], [7, 5]] is 1.**

The 2 by 2 matrix determinant follows the theorem known as the "Laplace's theorem" or "Laplace expansion theorem." It states that the determinant of a matrix can be calculated by **expanding along any row or column and taking the sum of the products of the elements with their corresponding cofactors**.

However, for 2 by 2 matrices, the determinant formula suffices, **where the product of the diagonal elements is subtracted from the product of the off-diagonal elements.**

Find the determinant of the matrix A = [3 2; -1 4].

Determine the value of the determinant for the matrix B = [5 -2; 7 -1].

Calculate the determinant for the matrix C = [-2 0; 6 3].

Find the determinant of the matrix D = [1/2 3; -5/4 2].

Determine the value of the determinant for the matrix E = [0 -1/2; 4 1/3].

Calculate the determinant for the matrix F = [2 -5; -3 7/4].

Find the determinant of the matrix G = [6 4; -2 -3].

Determine the value of the determinant for the matrix H = [1 2; 3/2 4/3].

Calculate the determinant for the matrix I = [-7 1; 1/5 -3/2].

Find the determinant of the matrix J = [0 3; -2 0].

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