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.

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CCSS.HSN.VM.C.8

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.

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CCSS.HSN.VM.C.8

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

• 3 x 3

• 3 x 2

• 2 x 2

• 2 x 3

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CCSS.HSN.VM.C.8

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.

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CCSS.HSN.VM.C.8

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

• -26

• -17

• 15

• 6

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CCSS.HSN.VM.C.8

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.

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CCSS.HSN.VM.C.8

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

• 22

• 15

• 0

• -20

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CCSS.HSN.VM.C.8

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.

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CCSS.HSN.VM.C.9

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.

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CCSS.HSN.VM.C.8

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

• -2

• 22

• 0

• 15

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CCSS.HSN.VM.C.8