Question

Which of the answer choices has matrix multiplication defined?

Answer 1

The answer choices that has matrix multiplication defined is

b. BC

What is the rule of matrix multiplication

The rule for matrix multiplication involves multiplying the elements of two matrices to produce a new matrix.

For matrix multiplication to be defined:

• the number of columns in the first matrix must be equal to the number of rows in the second matrix.

Applying this rule, we can see that number of columns in matrix B is 3 and the number of rows in matrix C is 3.

Since both are equal, matrix multiplication is defined

Answer 2

b. BC

Explanation:

The first thing is to calculate the dimensions of each matrix, that is, the number of rows x number of columns:

dimensions of A: 2x2

B dimensions: 2x3

C dimensions: 3x3

D dimensions: 1x3

We have that a matrix multiplication is defined, the internal numbers of its dimensions must be the same: we analyze each option:

BA: (2x3) * (2x2): the internal numbers do not match (a 3 for B and a 2 for A), so the multiplication of the matrix is not defined

BC: (2x3) * (3x3): the internal numbers are both 3, so the matrix multiplication is defined

CB: (3x3 ) * (2x3): the internal numbers do not match (a 3 for C and a 2 for B), so the multiplication of the matrix is not defined

CD: (3x3) * (1x3): the internal numbers do not match (a 3 for C and a 1 for D) so the multiplication of the matrix is not defined

Therefore the answer is b. BC