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3.6 Multiplying Matrices

3.6 Multiplying Matrices. Objective: You will multiply matrices. In order to multiply matrices. A • B = AB. m x n. m x p. n x p. Ex 1. Can you multiply? What will the dimensions be?. A. B. AB. 2 x 3. 3 x 4. 2 x 4. AB. A. B. 5 x 3. 5 x 2. Not possible.

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3.6 Multiplying Matrices

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  1. 3.6 Multiplying Matrices Objective: You will multiply matrices.

  2. In order to multiply matrices... A • B = AB m xn m x p nx p Ex 1. Can you multiply? What will the dimensions be? A B AB 2 x 3 3 x 4 2 x 4 AB A B 5 x 3 5 x 2 Not possible

  3. How to multiply... ac ad = 2 x 1 1 x 2 2 x 2

  4. How to multiply... ac ad = bc bd 2 x 1 1 x 2 2 x 2

  5. Ex. 1

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

  7. Ex. 3 FindBA

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

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

  10. Ex. 4 -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

  11. If we are multiplying matrices, we multiply each row of the first matrix by each column in the second matrix!! multiply each row of the first matrix by each column in the second matrix!! + + 1 + + 2 + + 1 + +

  12. 2 X 3 3 X 3 2(3)+(-3)(8)+5(-3) 2(9)+(-3)(0)+ 5(1) 2(1)+(-3)(-4)+ 5(5) -1(3)+(6)(8)+8(-3) -1(9)+(6)(0)+ 8(1) -1(1)+(6)(-4)+ 8(5)

  13. Ex. 5

  14. What are your questions?

  15. Assignment

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