In Exercises 9 - 16, find the following matrices: a. A + B

Verified step by step guidance

1. Step 1: Identify the matrices A and B. Here, A = [6 2 -3] and B = [4 -2 3]. Both are 1x3 matrices (one row, three columns).
2. Step 2: Understand that matrix addition requires matrices to be of the same dimension. Since both A and B are 1x3, we can add them element-wise.
3. Step 3: Add the corresponding elements of matrices A and B: add the first elements (6 + 4), the second elements (2 + (-2)), and the third elements (-3 + 3).
4. Step 4: Write the resulting matrix from the sums of each corresponding element to get A + B.
5. Step 5: Express the final matrix as a 1x3 matrix with the sums calculated in the previous step.

Key Concepts

Matrix Addition

Matrix addition involves adding corresponding elements from two matrices of the same dimensions. Each element in the resulting matrix is the sum of elements in the same position from the original matrices. For example, if A and B are both 1x3 matrices, then (A + B) is also a 1x3 matrix where each element is A[i] + B[i].

Matrix Dimensions and Compatibility

To add two matrices, they must have the same dimensions, meaning the same number of rows and columns. If matrices differ in size, addition is undefined. In this problem, both A and B are 1x3 matrices, so addition is possible and straightforward.

Representation of Matrices

Matrices are rectangular arrays of numbers arranged in rows and columns. They can represent data or systems of equations. Understanding how to read and write matrices, such as A = [6 2 -3], is essential for performing operations like addition or multiplication.