Math Problem Statement
Let B = [[1, 1, 2], [2, 3, 5], [3, 3, 7]], C = [[5, 4], [13, 11], [16, 14]], what is B^{-1}C?
Solution
The question asks to compute , where:
1 & 1 & 2 \\ 2 & 3 & 5 \\ 3 & 3 & 7 \end{bmatrix}, \quad C = \begin{bmatrix} 5 & 4 \\ 13 & 11 \\ 16 & 14 \end{bmatrix}$$ ### Steps to Solve: 1. **Find $$B^{-1}$$ (the inverse of matrix $$B$$):** - First, calculate the determinant of matrix $$B$$. - If the determinant is non-zero, use the adjugate method or other methods (like Gaussian elimination) to find the inverse of $$B$$. 2. **Multiply $$B^{-1}$$ by matrix $$C$$:** - After obtaining $$B^{-1}$$, compute the matrix product $$B^{-1}C$$. Let's start by computing $$B^{-1}$$. I'll calculate the inverse and the final product for you.The result of $$B^{-1}C$$ is: $$B^{-1}C = \begin{bmatrix} 1 & -1 \\ 2 & 1 \\ 1 & 2 \end{bmatrix}$$ Would you like further details on any of the steps, or have any questions about the solution? Here are some related questions you might explore: 1. How do you calculate the determinant of a 3x3 matrix? 2. What are the conditions for a matrix to be invertible? 3. Can all matrices be inverted? 4. How would you solve this problem using Gaussian elimination? 5. How do matrix operations, like multiplication, work for different matrix dimensions? **Tip:** The inverse of a matrix exists only if the determinant is non-zero!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Inversion
Matrix Multiplication
Formulas
B^{-1} = adj(B)/det(B)
Matrix Multiplication: AB = C
Theorems
Inverse Matrix Theorem
Determinant Calculation
Suitable Grade Level
College Level / Advanced High School (Grades 11-12)