Math Problem Statement

Let D be the matrix \[ \begin{bmatrix} -2 & -3 & -1 \\ -5 & -13 & 6 \\ -12 & -10 & 9 \end{bmatrix} \]

Solution

The matrix DD from the image is:

-2 & -3 & -1 \\ -5 & -13 & 6 \\ -12 & -10 & 9 \end{bmatrix}$$ Would you like to calculate the determinant, inverse, or perform another operation with this matrix? Let me know how you'd like to proceed. Here are some possible follow-up questions you may be interested in: 1. How do you compute the determinant of matrix $$D$$? 2. Is matrix $$D$$ invertible? 3. What are the eigenvalues of matrix $$D$$? 4. How do you find the rank of matrix $$D$$? 5. What does it mean if the determinant of matrix $$D$$ is zero? **Tip**: The determinant of a matrix can help you understand if the matrix is invertible or singular.

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Math Problem Analysis

Mathematical Concepts

Matrix Algebra
Determinants
Inverses
Eigenvalues

Formulas

Determinant of a 3x3 matrix: det(D) = a(ei − fh) − b(di − fg) + c(dh − eg)
Inverse of a matrix: A^(-1) = adj(A)/det(A)
Eigenvalues: Solving det(D − λI) = 0

Theorems

Determinant theorem for square matrices
Invertibility theorem: A matrix is invertible if and only if its determinant is non-zero

Suitable Grade Level

Grades 11-12 or undergraduate level

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