Math Problem Statement
⎡ ⎢ ⎣ − 5 − 7 − 4 − 8 1 − 2 6 − 1 − 10 ⎤ ⎥ ⎦
⋅
⎡ ⎢ ⎣ 1 0 0 0 1 0 0 0 1 ⎤ ⎥ ⎦ =
Solution
The given matrix multiplication involves multiplying a 3x3 matrix by a 3x3 identity matrix. Recall that multiplying any matrix by the identity matrix of the same size results in itself.
Thus, we can directly conclude that:
-5 & -7 & -4 \\ -8 & 1 & -2 \\ 6 & -1 & -10 \end{bmatrix} \cdot \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} = \begin{bmatrix} -5 & -7 & -4 \\ -8 & 1 & -2 \\ 6 & -1 & -10 \end{bmatrix}$$ ### Final Answer: $$\begin{bmatrix} -5 & -7 & -4 \\ -8 & 1 & -2 \\ 6 & -1 & -10 \end{bmatrix}$$ Let me know if you would like me to demonstrate the calculations or provide further explanations. --- Here are 5 related questions for further exploration: 1. What happens when you multiply a matrix by a non-identity diagonal matrix? 2. How can the identity matrix be used to solve linear systems? 3. What are the properties of the identity matrix in matrix algebra? 4. How would the result change if the order of multiplication was reversed? 5. How do matrix transformations relate to the identity matrix? **Tip:** When working with matrices, always confirm their dimensions are compatible for multiplication before proceeding!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Multiplication
Identity Matrix
Linear Algebra
Formulas
Matrix multiplication formula: (AB)ij = Σ(Aik × Bkj)
Theorems
Identity Matrix Property: A × I = A
Suitable Grade Level
Grades 10-12