How to Calculate the Determinant of a 2×2 Matrix

Math Problem Statement

Determinan matriks ordo 2×2

Determinant of a 2×2 matrix can be calculated using the following formula:

For a matrix:

a & b \\ c & d \end{pmatrix}$$ The determinant, denoted as $$\text{det}(A)$$, is given by: $$\text{det}(A) = (a \times d) - (b \times c)$$ ### Example: For the matrix: $$\begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix}$$ The determinant is: $$\text{det}(A) = (2 \times 5) - (3 \times 4) = 10 - 12 = -2$$ Would you like further details on the determinant calculation, or do you have any questions? --- Here are some related questions: 1. How do you calculate the determinant for a 3×3 matrix? 2. What are some applications of the determinant in linear algebra? 3. What does it mean when the determinant of a matrix is zero? 4. How can you compute the determinant of larger matrices using cofactor expansion? 5. What is the geometric interpretation of the determinant of a matrix? **Tip:** The determinant of a 2×2 matrix tells you the area scaling factor when the matrix is applied as a transformation on a plane.

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Linear Algebra
Determinants
Matrix Operations

det(A) = (a × d) - (b × c) for a 2×2 matrix

Determinant Calculation for 2×2 Matrices

Grades 9-12

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