Math Problem Statement

Calculate properties or perform operations on the given 3x3 matrix: \[ \begin{bmatrix} 2 & 1 & 5 \\ 8 & 2 & -3 \\ -4 & 1 & 6 \end{bmatrix} \]

Solution

The image represents a 3x3 matrix:

2 & 1 & 5 \\ 8 & 2 & -3 \\ -4 & 1 & 6 \end{bmatrix}$$ Let me know if you'd like to calculate: 1. The determinant of the matrix. 2. The inverse of the matrix (if it exists). 3. Eigenvalues or eigenvectors. 4. Solving a linear system using this matrix. 5. Any other operations with this matrix. ### Tip: The determinant of a 3x3 matrix can be calculated using cofactor expansion across any row or column.

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Operations
Determinants
Matrix Inversion

Formulas

Determinant of a 3x3 matrix: \( \text{det}(A) = a(ei − fh) − b(di − fg) + c(dh − eg) \)
Inverse of a matrix: \( A^{-1} = \frac{1}{\text{det}(A)} \text{adj}(A) \), if \( \text{det}(A) \neq 0 \)

Theorems

Cramer's Rule
Properties of Determinants
Existence of Inverses

Suitable Grade Level

Undergraduate (Linear Algebra) or Advanced High School (AP Math)

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