Matrix Multiplication Concepts and Properties

This video tutorial explains matrix multiplication, focusing on the product of Matrix B and Matrix A. It highlights the importance of the order in matrix multiplication, as it affects the dimensions of the resulting matrix. The tutorial provides a detailed step-by-step calculation of the elements in the resulting 3x3 matrix, using rows from the first matrix and columns from the second. It also compares the results of B x A and A x B, emphasizing that matrix multiplication is not commutative. The video concludes with a summary and additional notes on the topic.

Why does the order of matrix multiplication matter?

• Because it determines the speed of calculation.

• Because it changes the color of the matrix.

• Because it affects the type of matrix.

• Because it affects the dimensions of the resulting matrix.

What must be true for matrix multiplication to be defined?

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

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

• Both matrices must be square matrices.

• Both matrices must have the same number of elements.

What are the dimensions of the product matrix B x A?

• 3 x 3

• 3 x 2

• 2 x 2

• 2 x 3

How do you determine the element in the first row and first column of the product matrix?

• By dividing the first row of the first matrix by the first column of the second matrix.

• By multiplying the first row of the first matrix with the first column of the second matrix and summing the products.

• By adding the elements of the first row of the first matrix.

• By subtracting the first column of the second matrix from the first row of the first matrix.

What is the value of the element in the second row and third column of the product matrix?

• -26

• -17

• 15

• 6

Which row and column are used to find the element in the third row and second column of the product matrix?

• First row of the first matrix and third column of the second matrix.

• Second row of the first matrix and third column of the second matrix.

• Third row of the first matrix and second column of the second matrix.

• Third row of the first matrix and first column of the second matrix.

What is the result of the calculation for the element in the third row and first column?

• 22

• 15

• 0

• -20

How does the product matrix B x A compare to A x B in terms of dimensions?

• B x A is 2 x 2, while A x B is 3 x 3.

• Both are 2 x 2.

• Both are 3 x 3.

• B x A is 3 x 3, while A x B is 2 x 2.

What does the comparison between B x A and A x B illustrate about matrix multiplication?

• Matrix multiplication is distributive.

• Matrix multiplication is not commutative.

• Matrix multiplication is associative.

• Matrix multiplication is commutative.

What is the final element value in the third row and third column of the product matrix?

• -2

• 22

• 0

• 15