Mastering Matrix Multiplication Techniques

What must be true about the number of columns in the first matrix and the number of rows in the second matrix for them to be multiplied?

• The first must be greater than the second.

• The second must be greater than the first.

• They must be equal.

• They must be different.

If you have a 2x3 matrix and a 3x1 matrix, can they be multiplied?

• No, because the number of rows in the first matrix does not equal the number of columns in the second matrix.

• Yes, because the number of columns in the first matrix equals the number of rows in the second matrix.

• Yes, because the number of rows in the first matrix equals the number of columns in the second matrix.

• No, because the number of columns in the first matrix does not equal the number of rows in the second matrix.

What is the first step in multiplying two matrices once you have confirmed they can be multiplied?

• Add the two matrices.

• Subtract the second matrix from the first.

• Write down the second matrix as is.

• Transpose the first matrix.

When multiplying matrices, how do you handle the rows and columns?

• Subtract the columns of the second matrix from the rows of the first matrix.

• Write the first row of the first matrix as a column and multiply it by the columns of the second matrix.

• Add the rows of the first matrix to the columns of the second matrix.

• Write the first column of the first matrix as a row and multiply it by the rows of the second matrix.

In the example given, what is the result of multiplying the first row of the first matrix by the first column of the second matrix?

• Negative 12

• 39

• 3

• Negative 6

What is the result of multiplying the second row of the first matrix by the first column of the second matrix?

• 35

• 39

• 3

• 4

In the second example, what is the result of multiplying the first row of the first matrix by the second column of the second matrix?

• Negative 20

• 14

• 0

• Negative 4

What is the result of multiplying the second row of the first matrix by the third column of the second matrix?

• Negative 6

• 26

• 5

• 21

How do you determine the size of the resulting matrix after multiplication?

• By the number of rows in both matrices.

• By the number of columns in both matrices.

• By the number of columns in the first matrix and the number of rows in the second matrix.

• By the number of rows in the first matrix and the number of columns in the second matrix.

If you multiply a 2x2 matrix with a 2x3 matrix, what will be the size of the resulting matrix?

• 2x3

• 2x2

• 3x3

• 3x2