Math Problem Statement
Calculate the determinant of the following 2x2 matrix:
\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}
Solution
The image asks to calculate the determinant of the following matrix:
1 & 2 \\ 3 & 4 \end{pmatrix}$$ The determinant of a 2x2 matrix $$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$ is given by the formula: $$\text{det}(A) = ad - bc$$ For the given matrix: $$\text{det}\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} = (1)(4) - (2)(3) = 4 - 6 = -2$$ Thus, the determinant of the matrix is **-2**. Would you like more details on how matrix determinants work? Here are some related questions: 1. How do you compute the determinant of a 3x3 matrix? 2. What properties of a matrix can be derived from its determinant? 3. Can a matrix with a determinant of zero be inverted? 4. How is the determinant used in solving systems of linear equations? 5. How do eigenvalues relate to the determinant of a matrix? **Tip:** For a square matrix of any size, a zero determinant indicates that the matrix is singular and cannot be inverted.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Determinants
Formulas
Determinant of 2x2 matrix: det(A) = ad - bc
Theorems
Determinant theorem for 2x2 matrices
Suitable Grade Level
Grades 9-12