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3.6 Multiply Matrices

3.6 Multiply Matrices. Objectives: Analyze situations using algebraic symbols Use representation to solve problems Understand the properties of matrices with respect to multiplication. Multiply two matrices. Common Core Standards: A-REI-6, N-VM-8, N-VM-12 Assessments:

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3.6 Multiply Matrices

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  1. 3.6 Multiply Matrices Objectives: Analyze situations using algebraic symbols Use representation to solve problems Understand the properties of matrices with respect to multiplication. Multiply two matrices. Common Core Standards: A-REI-6, N-VM-8, N-VM-12 Assessments: Define all vocab from this section 3-6 worksheet

  2. In Lesson 4-1, you multiplied matrices by a number called a scalar. You can also multiply matrices together. The product of two or more matrices is the matrix product. The following rules apply when multiplying matrices. • Matrices A and B can be multiplied only if the number of columns in A equals the number of rows in B. • The product of an mnand an npmatrix is an mpmatrix.

  3. An m n matrix A can be identified by using the notation Am n.

  4. Tell whether the product is defined. If so, give its dimensions. A3  4 and B4  2; AB

  5. Tell whether the product is defined. If so, give its dimensions. C1  4 and D3  4; CD

  6. Find the product, if possible. WX Check the dimensions.

  7. Multiply row 1 of W and column 1 of X as shown. Place the result in wx11. 3(4) + –2(5)

  8. Example 2A Continued Multiply row 1 of W and column 2 of X as shown. Place the result in wx12. 3(7) + –2(1)

  9. Example 2A Continued Multiply row 1 of W and column 3 of X as shown. Place the result in wx13. 3(–2) + –2(–1)

  10. Example 2A Continued Multiply row 2 of W and column 1 of X as shown. Place the result in wx21. 1(4) + 0(5)

  11. Example 2A Continued Multiply row 2 of W and column 2 of X as shown. Place the result in wx22. 1(7) + 0(1)

  12. Example 2A Continued Multiply row 2 of W and column 3 of X as shown. Place the result in wx23. 1(–2) + 0(–1)

  13. Example 2A Continued Multiply row 3 of W and column 1 of X as shown. Place the result in wx31. 2(4) + –1(5)

  14. Example 2A Continued Multiply row 3 of W and column 2 of X as shown. Place the result in wx32. 2(7) + –1(1)

  15. Example 2A Continued Multiply row 3 of W and column 3 of X as shown. Place the result in wx33. 2(–2) + –1(–1)

  16. Find each product, if possible. XW Check the dimensions.

  17. Find each product, if possible. XY Check the dimensions.

  18. Two stores held sales on their videos and DVDs, with prices as shown. Use the sales data to determine how much money each store brought in from the sale on Saturday. Use a product matrix to find the sales of each store for each day.

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