Question

Now change matrix B to a 3x3 matrix and enter these values for B, then select A • B to calculate the product.

a) A • B is not defined
b) A • B is a 2x3 matrix
c) A • B is a 3x2 matrix
d) A • B is a 2x2 matrix

Answer 1

The product of matrix A with a 3x3 matrix B can either result in a 2x3 matrix if A is a 2x3 matrix, or it is undefined if A is a 2x2 matrix. Without knowing the dimensions of matrix A, we cannot definitively answer the question.

Step-by-step explanation:

The question is about the multiplication of matrices, specifically finding the product of matrix A with a changed matrix B, where B is now a 3x3 matrix. For two matrices to be multiplicable, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Since matrix A's size is not provided in the question, the correct answer cannot be determined without that information. However, the general rule is:

• If A is a 2x3 matrix and B is a 3x3 matrix, the product A • B is defined and the result is a 2x3 matrix.
• If A is a 2x2 matrix and B is a 3x3 matrix, then A • B is not defined because the number of columns in A does not equal the number of rows in B.

Therefore, the correct answer could be 'A • B is a 2x3 matrix' if A is a 2x3 matrix or 'A • B is not defined' if A is a 2x2 matrix.