Math Problem Statement

Diberikan matriks A = [2 3; 1 4] dan matriks B = [1 2; 5 6]. Apa hasil dari A + B?

Solution

The image shows two matrices, A=[2314]A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} and B=[1256]B = \begin{bmatrix} 1 & 2 \\ 5 & 6 \end{bmatrix}, and the question asks for the result of A+BA + B.

Matrix Addition

Matrix addition is done element-wise. That means, to add two matrices, you add their corresponding elements. The matrices AA and BB are both 2x2 matrices, so we can add them as follows:

A+B=[2314]+[1256]=[2+13+21+54+6]=[35610]A + B = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} + \begin{bmatrix} 1 & 2 \\ 5 & 6 \end{bmatrix} = \begin{bmatrix} 2+1 & 3+2 \\ 1+5 & 4+6 \end{bmatrix} = \begin{bmatrix} 3 & 5 \\ 6 & 10 \end{bmatrix}

Thus, the result of A+BA + B is [35610]\begin{bmatrix} 3 & 5 \\ 6 & 10 \end{bmatrix}.

This matches option a from the image.

Would you like more details on matrix operations? Here are 5 additional questions to explore:

  1. How do you subtract two matrices?
  2. What is matrix multiplication and how does it differ from matrix addition?
  3. Can you explain the conditions under which matrix addition is possible?
  4. How do scalar multiplication and matrix addition interact?
  5. What are some real-world applications of matrix operations?

Tip: When adding or subtracting matrices, they must be of the same dimension.

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Math Problem Analysis

Mathematical Concepts

Matrix addition
Linear algebra

Formulas

Matrix addition: A + B = [a_11 + b_11, a_12 + b_12; a_21 + b_21, a_22 + b_22]

Theorems

Matrix element-wise addition

Suitable Grade Level

Grades 9-12