Math Problem Statement

Jika A = (3 4, 2 -1) dan B = (0 3, 1 5), maka hasil dari A + B = ....

Solution

The problem provides two matrices, AA and BB, and asks for the result of their addition, A+BA + B.

Given:

\quad \text{and} \quad B = \begin{pmatrix} 0 & 3 \\ 1 & 5 \end{pmatrix}$$ The sum of two matrices is found by adding corresponding elements from both matrices. So, let's compute: $$A + B = \begin{pmatrix} 3+0 & 4+3 \\ 2+1 & -1+5 \end{pmatrix}$$ $$A + B = \begin{pmatrix} 3 & 7 \\ 3 & 4 \end{pmatrix}$$ Thus, the result of $$A + B$$ is: $$\boxed{\begin{pmatrix} 3 & 7 \\ 3 & 4 \end{pmatrix}}$$ Let me know if you'd like more details or have any questions! Here are some related questions: 1. How do you perform matrix subtraction? 2. What happens when you multiply matrices instead of adding them? 3. Can matrix addition be performed with matrices of different dimensions? 4. What are the properties of matrix addition? 5. How would the solution change if one of the matrix elements were zero matrices? **Tip**: When adding matrices, always ensure that both matrices have the same dimensions.

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Math Problem Analysis

Mathematical Concepts

Matrix Addition

Formulas

Matrix addition: A + B = (a11 + b11 a12 + b12; a21 + b21 a22 + b22)

Theorems

Matrix addition is defined for matrices of the same dimension.

Suitable Grade Level

Grades 10-12