Question

If A is a 2x2 matrix and B is a 2x1 matrix, what is the dimension of AB?

Answer 1

The product of a 2x2 matrix A and a 2x1 matrix B is a 2x1 matrix as per matrix multiplication rules.

Step-by-step explanation:

The dimension of the product of a 2x2 matrix A and a 2x1 matrix B will be a 2x1 matrix. This result comes from matrix multiplication rules where the number of rows in the resulting matrix comes from the first (left) matrix, and the number of columns comes from the second (right) matrix. Since matrix A has 2 rows and matrix B has 1 column, the resulting matrix AB will have 2 rows and 1 column.

Answer 2

2x2 matrix

Step-by-step explanation:

Given

Dimension of matrices A = 2x2 matrix

Dimension of matrices B = 2x1 matrix

The dimension of matrix AB can be gotten by cancelling the row of matrices 1 and column of matrices 2.

After cancelling both row and column, the remaining dimension will be 2x2 matrix. Hence the dimension of AB is 2x2 matrix