Math Problem Statement
What is the determinant of the matrix [6, 8; 3, 7]?
Solution
The problem asks for the determinant of the matrix:
6 & 8 \\ 3 & 7 \end{bmatrix}$$ The determinant of a $$2 \times 2$$ matrix $$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$ is calculated using the formula: $$\text{Determinant} = (a \cdot d) - (b \cdot c)$$ For the given matrix: $$a = 6, \, b = 8, \, c = 3, \, d = 7$$ Substitute these values into the formula: $$\text{Determinant} = (6 \cdot 7) - (8 \cdot 3)$$ $$\text{Determinant} = 42 - 24 = 18$$ ### Final Answer: The determinant of the matrix is **18**. Would you like additional details or have any other questions? --- Here are 5 related questions to expand your understanding: 1. How do you calculate the determinant of a $$3 \times 3$$ matrix? 2. What is the geometric significance of the determinant in two-dimensional transformations? 3. Can the determinant of a matrix be zero? What does that signify? 4. How is the determinant used in solving systems of linear equations (Cramer's Rule)? 5. What happens to the determinant when rows or columns of a matrix are swapped? **Tip:** Remember, a matrix with a determinant of zero is called "singular," meaning it does not have an inverse!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrices
Determinants
Formulas
Determinant of a 2x2 matrix formula: det(A) = ad - bc
Theorems
Determinant properties of 2x2 matrices
Suitable Grade Level
Grades 9-12