Math Problem Statement
Simplify the sum of two matrices: [1 2 1; 3 4 0] + [4 2 0; 1 0 0; 3 0 0].
Solution
The question asks you to simplify the sum of two matrices:
1 & 2 & 1 \\ 3 & 4 & 0 \end{bmatrix} + \begin{bmatrix} 4 & 2 & \\ 1 & 0 & 0 \\ 3 & 0 \end{bmatrix}$$ To add two matrices, simply add their corresponding elements. Let's perform the addition: 1. First row, first element: $$1 + 4 = 5$$ 2. First row, second element: $$2 + 2 = 4$$ 3. First row, third element: $$1 + 0 = 1$$ 4. Second row, first element: $$3 + 1 = 4$$ 5. Second row, second element: $$4 + 0 = 4$$ 6. Second row, third element: $$0 + 0 = 0$$ So the result of the matrix addition is: $$\begin{bmatrix} 5 & 4 & 1 \\ 4 & 4 & 0 \end{bmatrix}$$ Now, let's compare this result with the answer options. The correct answer matches option **B**. Do you have any questions or would you like further explanation? Here are five related questions: 1. How do you perform matrix subtraction? 2. What are the conditions for adding two matrices? 3. How do you multiply two matrices? 4. Can you add a 2x3 matrix with a 3x2 matrix? 5. What is the identity matrix in linear algebra? **Tip:** For matrix addition, both matrices must have the same dimensions, otherwise the operation is undefined.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix addition
Linear algebra
Formulas
Matrix addition: Add corresponding elements of two matrices
Theorems
Matrix operations theorem for addition: Matrices must have the same dimensions to be added.
Suitable Grade Level
Grades 9-12