Multiply matrices Use the properties of matrix multiplication.

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Presentation transcript:

Multiply matrices Use the properties of matrix multiplication.

Rules for multiplying matrices 1.The # of columns in the first matrix must be equal to the # of rows in the second matrix. 2.The elements in the rows of the first matrix are multiplied to the corresponding elements in the columns of the second matrix. 3. Add all the multiplication problems together and put the answer in the corresponding(row #, column #) in the answer matrix. 4.Continue to multiply each row(1 st matrix) to each column(2 nd matrix).

Key Concept a ₁ b ₁ x ₁ y ₁ a ₁ x ₁ + b ₁ x ₂ a ₁ y ₁ + b ₁ y ₂ a ₂ b ₂ x ₂ y ₂ a ₂ x ₁ + b ₂ x ₂ a ₂ y ₁ + b ₂ y ₂ 2x2 2x22x2 Could you multiply? If yes what are the dimensions of the answer matrix? 1) A3x1 B1x5 2) M4x2 N3x2 3) J5x3 K3x1 4) A6x4 B4x7 5) R4x5 T4x2

Associative Prop. Of Matrix Multiplication (AB)C = A(BC) Associative Prop. Of Scalar Multiplication c(AB) = (cA)B = A(cB) Note c is a constant Left Distributive Property C(A + B) = CA + CB Right Distributive Property (A + B)C = AC + BC *** Make sure you can multiply the matrices