If A is a 2x2 matrix and B is a 2x3 matrix, what is the order of the product AB?
Practice Questions
Q1
If A is a 2x2 matrix and B is a 2x3 matrix, what is the order of the product AB? (2019)
2x2
2x3
3x2
2x5
Questions & Step-by-Step Solutions
If A is a 2x2 matrix and B is a 2x3 matrix, what is the order of the product AB? (2019)
Step 1: Identify the dimensions of matrix A. A is a 2x2 matrix, which means it has 2 rows and 2 columns.
Step 2: Identify the dimensions of matrix B. B is a 2x3 matrix, which means it has 2 rows and 3 columns.
Step 3: Check if the matrices can be multiplied. For two matrices to be multiplied, the number of columns in the first matrix (A) must equal the number of rows in the second matrix (B). Here, A has 2 columns and B has 2 rows, so they can be multiplied.
Step 4: Determine the dimensions of the resulting product matrix AB. The number of rows in the product will be the same as the number of rows in A (which is 2), and the number of columns will be the same as the number of columns in B (which is 3).
Step 5: Conclude that the order of the product AB is 2x3.
