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

Verified step by step guidance

1. Step 1: Identify the matrices A and B. Matrix A is \( \begin{bmatrix} 1 & 3 \\ 3 & 4 \\ 5 & 6 \end{bmatrix} \) and matrix B is \( \begin{bmatrix} 2 & -1 \\ 3 & -2 \\ 0 & 1 \end{bmatrix} \).
2. Step 2: Confirm that both matrices have the same dimensions. Matrix A is 3x2 and matrix B is also 3x2, so subtraction is possible.
3. Step 3: Subtract matrix B from matrix A by subtracting corresponding elements. For each element in the resulting matrix \( C = A - B \), calculate \( c_{ij} = a_{ij} - b_{ij} \).
4. Step 4: Perform the element-wise subtraction: For example, the element in the first row and first column is \( 1 - 2 \), the first row and second column is \( 3 - (-1) \), and so on for all elements.
5. Step 5: Write the resulting matrix after subtraction by placing all the calculated elements in their respective positions to form the matrix \( A - B \).

Key Concepts

Matrix Subtraction

Matrix subtraction involves subtracting corresponding elements of two matrices of the same dimensions. Each element in the resulting matrix is found by subtracting the element in matrix B from the element in matrix A at the same position.

Matrix Dimensions

For two matrices to be added or subtracted, they must have the same number of rows and columns. This ensures that each element in one matrix has a corresponding element in the other matrix for the operation.

Representation of Matrices

Matrices are rectangular arrays of numbers arranged in rows and columns. Understanding how to read and interpret matrix notation is essential for performing operations like addition, subtraction, and multiplication.