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4-2. Multiplying Matrices. Warm Up. Lesson Presentation. Lesson Quiz. Holt Algebra 2. Warm Up. 1. What are the dimensions of A? 2. What is entry D 12 ? Evaluate if possible. 3. 2A — C 4. C + 2D 5. 10(2B + D). 3  2. –2. Not possible. Objectives.

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  1. 4-2 Multiplying Matrices Warm Up Lesson Presentation Lesson Quiz Holt Algebra 2

  2. Warm Up 1. What are the dimensions of A? 2. What is entry D12? Evaluate if possible. 3. 2A — C 4. C + 2D 5. 10(2B + D) 3  2 –2 Not possible

  3. Objectives Understand the properties of matrices with respect to multiplication. Multiply two matrices.

  4. Vocabulary matrix product square matrix main diagonal multiplicative identity matrix

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

  6. Example 1A: Identifying Matrix Products Tell whether the product is defined. If so, give its dimensions. A3  4 and B4  2; AB A B AB 3442 = 3  2 matrix The inner dimensions are equal (4 = 4), so the matrix product is defined. The dimensions of the product are the outer numbers, 3  2.

  7. Example 1B: Identifying Matrix Products Tell whether the product is defined. If so, give its dimensions. C1  4 and D3  4; CD C D 1434 The inner dimensions are not equal (4 ≠ 3), so the matrix product is not defined.

  8. Check It Out! Example 1c Tell whether the product is defined. If so, give its dimensions. P2  5 Q5  3 R4  3 S4  5 SQ S Q 4553 The inner dimensions are equal (5 = 5), so the matrix product is defined. The dimensions of the product are the outer numbers, 4  3.

  9. Example 2A: Finding the Matrix Product Find the product, if possible. WX Check the dimensions. W is 3  2 , X is 2  3 . WX is defined and is 3  3.

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

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

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

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

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

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

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

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

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

  19. Example 2B: Finding the Matrix Product Find each product, if possible. XW Check the dimensions. X is 2 3, and W is 3 2 so the product is defined and is 2  2.

  20. Check It Out! Example 2a Find the product, if possible. BC Check the dimensions. B is 3 2, and C is 2 2 so the product is defined and is 3  2.

  21. Lesson Quiz Evaluate if possible. 1.AB 2.BA 3.A2 4.BD 5.C3

  22. Lesson Quiz Evaluate if possible. 1.AB 2.BA 3.A2 4.BD 5.C3 not possible not possible

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