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

Verified step by step guidance

1. Step 1: Understand that to add two matrices, they must have the same dimensions. Here, matrix A and matrix B are both 3x2 matrices, so addition is possible.
2. Step 2: Write down the matrices explicitly: A = \begin{bmatrix} 1 & 3 \\ 3 & 4 \\ 5 & 6 \end{bmatrix}, B = \begin{bmatrix} 2 & -1 \\ 3 & -2 \\ 0 & 1 \end{bmatrix}
3. Step 3: Add the corresponding elements of matrices A and B. This means adding each element in the first row and first column of A to the element in the first row and first column of B, and so on for all elements.
4. Step 4: Express the sum matrix C = A + B as: C = \begin{bmatrix} 1+2 & 3+(-1) \\ 3+3 & 4+(-2) \\ 5+0 & 6+1 \end{bmatrix}
5. Step 5: Simplify each element in the resulting matrix to get the final matrix sum (do not calculate the final values here, just set up the expression).

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. This operation is only defined when both matrices have the same number of rows and columns.

Matrix Dimensions

The dimension of a matrix is given by the number of rows and columns it contains, expressed as 'rows × columns'. For matrix addition to be valid, both matrices must have identical dimensions, ensuring each element has a corresponding element to add.

Element-wise Operations

Element-wise operations on matrices, such as addition, require performing the operation on each pair of corresponding elements individually. Understanding this concept helps in correctly computing the sum of matrices by focusing on each element's position.