Given A = , B = <2x3 Matrix>, and C = <3x2 Matrix>, find each product, ifpossible. See Examples 5–7. AB

Verified step by step guidance

1. Step 1: Understand Matrix Multiplication Compatibility
2. Step 2: Determine the Dimensions of Matrices A, B, and C
3. Step 3: Check if the Product AB is Possible
4. Step 4: Set Up the Multiplication of Matrices A and B
5. Step 5: Calculate the Entries of the Resulting Matrix AB

Key Concepts

Matrix Multiplication

Matrix multiplication involves taking the rows of the first matrix and the columns of the second matrix to produce a new matrix. For two matrices A (m x n) and B (n x p) to be multiplied, the number of columns in A must equal the number of rows in B. The resulting matrix will have dimensions m x p.

Matrix Dimensions

The dimensions of a matrix are defined by the number of rows and columns it contains, expressed as 'rows x columns'. Understanding matrix dimensions is crucial for determining whether two matrices can be multiplied. For example, a 2x3 matrix has 2 rows and 3 columns, while a 3x2 matrix has 3 rows and 2 columns.

Product of Matrices

The product of two matrices is calculated by summing the products of corresponding entries from the rows of the first matrix and the columns of the second matrix. This operation is only defined when the matrices meet the dimensional requirements for multiplication, resulting in a new matrix that encapsulates the combined information of the two original matrices.