Determinant of a 2×2 Matrix Calculator

This Determinant of a 2×2 Matrix Calculator helps you find the determinant of a 2×2 matrix and shows each step clearly. In Algebra 2, determinants are often used with matrices and systems of equations. The calculator works by multiplying the entries on one diagonal, multiplying the entries on the other diagonal, and then subtracting the second product from the first.

Step-by-step method

1. Write the 2×2 matrix in the form A = [[a, b], [c, d]].
2. Use the formula det( A ) = ad − bc.
3. Substitute the values and simplify.

Formula:

Example 1: Take the values below.

Step 1 - Write the 2×2 matrix in the form A = [[a, b], [c, d]].

In this problem: The entries are \(a = 3\), \(b = 8\), \(c = 4\), and \(d = 6\).

Step 2 - Use the formula det( A ) = ad − bc.

In this problem: For a 2×2 matrix, multiply the main diagonal and subtract the other diagonal product: \(\det(A) = ad - bc\).

Step 3 - Substitute the values and simplify.

In this problem: The determinant is \(-14\).

Final answer:

Example 2: Take the values below.

Step 1 - Write the 2×2 matrix in the form A = [[a, b], [c, d]].

In this problem: The entries are \(a = -2\), \(b = 5\), \(c = 1\), and \(d = 7\).

Step 2 - Use the formula det( A ) = ad − bc.

In this problem: For a 2×2 matrix, multiply the main diagonal and subtract the other diagonal product: \(\det(A) = ad - bc\).

Step 3 - Substitute the values and simplify.

In this problem: The determinant is \(-19\).

Final answer:

See Example 1 Hide Example 1

Problem

\(A = \begin{pmatrix} 3 & 8 \\ 4 & 6 \end{pmatrix}\)

Approach

Step-by-step method

1. Write the 2×2 matrix in the form A = [[a, b], [c, d]].
2. Use the formula det( A ) = ad − bc.
3. Substitute the values and simplify.

Step 1

Step 1 - Write the 2×2 matrix in the form A = [[a, b], [c, d]].

In this problem: The entries are \(a = 3\), \(b = 8\), \(c = 4\), and \(d = 6\).

\(A = \begin{pmatrix} 3 & 8 \\ 4 & 6 \end{pmatrix}\)

Step 2

Step 2 - Use the formula det( A ) = ad − bc.

In this problem: For a 2×2 matrix, multiply the main diagonal and subtract the other diagonal product: \(\det(A) = ad - bc\).

\(\det(A) = ad - bc\)

Step 3

Step 3 - Substitute the values and simplify.

In this problem: The determinant is \(-14\).

\(\det(A) = 3 \cdot 6 - 8 \cdot 4 = 18 - 32 = -14\)

Final Answer

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See Example 2 Hide Example 2

Problem

\(A = \begin{pmatrix} -2 & 5 \\ 1 & 7 \end{pmatrix}\)

Approach

Step-by-step method

1. Write the 2×2 matrix in the form A = [[a, b], [c, d]].
2. Use the formula det( A ) = ad − bc.
3. Substitute the values and simplify.

Step 1

Step 1 - Write the 2×2 matrix in the form A = [[a, b], [c, d]].

In this problem: The entries are \(a = -2\), \(b = 5\), \(c = 1\), and \(d = 7\).

\(A = \begin{pmatrix} -2 & 5 \\ 1 & 7 \end{pmatrix}\)

Step 2

Step 2 - Use the formula det( A ) = ad − bc.

In this problem: For a 2×2 matrix, multiply the main diagonal and subtract the other diagonal product: \(\det(A) = ad - bc\).

\(\det(A) = ad - bc\)

Step 3

Step 3 - Substitute the values and simplify.

In this problem: The determinant is \(-19\).

\(\det(A) = (-2) \cdot 7 - 5 \cdot 1 = -14 - 5 = -19\)

Final Answer

\(\)