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Matrix Multiplication: Understanding Dimensions and Operations

Learn how to multiply matrices, determine product dimensions, and execute operations correctly. Always verify matrix dimensions before multiplying. Practice with examples provided to enhance understanding.

skyler-barnett
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Matrix Multiplication: Understanding Dimensions and Operations

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  1. Warm-Up – October 7 1) 3) 2)

  2. 4.2 Multiplying Matrices

  3. In order to multiply matrices... A • B = AB m xn nx p m x p Ex 1. These MUST match Is the product defined? What are the dimensions of AB? A B AB 2 x 3 3 x 4 2 x 4 AB A B 5 x 3 5 x 2 Not defined

  4. How to multiply... Always check dimensions FIRST! ac ad = bd bc 2 x 1 1 x 2 2 x 2

  5. Ex. 1 -2 6 5 -15 2 x 1 1 x 2 2 x 2

  6. How to multiply... ag +bi +ck ah +bj +cm = 2 x 3 3 x 2 2 x 2

  7. How to multiply... ag +bi +ck ah +bj +cm = dg +ei +fk dh +ej +fm 2 x 3 3 x 2 2 x 2

  8. Ex. 2 Is the product defined? 2 x 2 3 x 2 -1(4) +5(6) -1(-3) +5(8) -4 + 30 3 + 40 20 +12 -15 + 16 5(4) +2(6) 5(-3) +2(8) = 0 + -24 0 + -32 0(4) +-4(6) 0(-3) +-4(8) 26 43 32 1 -24 -32

  9. STOP HERE for WEB!! Or look at more examples …..

  10. Ex. 3 FindAB -16 + 1 -12 +2 -15 -10 = 0 - 2 0 - 4 -2 - 4

  11. Ex. 4 FindBA

  12. Ex. 5 4 x 3 3 x 1 4 x 1

  13. Ex. 6 2 x 3 3 x 3

  14. Ex. 7

  15. What are your questions?

  16. Homework • Page 211: #4-20 ALL • Don’t work #10

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