Math Problem Statement

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Find the inverse of the following matrix: C = [[-1, 2, -1], [1, -3, 1], [1, -6, 2]]

Solution

The inverse of matrix CC is:

0 & 2 & -1 \\ -1 & -1 & 0 \\ -3 & -4 & 1 \end{pmatrix}$$ Looking at the provided options, this corresponds to option **c**. Would you like further clarification or a step-by-step explanation of how this inverse was computed? Here are 5 related questions for further practice: 1. How do you calculate the determinant of a 3x3 matrix? 2. What conditions must a matrix satisfy for its inverse to exist? 3. How do row operations relate to finding a matrix's inverse? 4. Can you find the inverse of a 2x2 matrix? 5. How do you interpret the inverse of a matrix geometrically? **Tip:** Always check the determinant before computing the inverse, as a matrix with a determinant of zero does not have an inverse.

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Math Problem Analysis

Mathematical Concepts

Matrix Algebra
Inverse of a Matrix
Linear Algebra

Formulas

Matrix inverse formula: A^-1 = adj(A) / det(A)
Determinant of a 3x3 matrix: det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)

Theorems

The Invertibility Theorem: A matrix is invertible if and only if its determinant is non-zero

Suitable Grade Level

College level / Advanced High School