4 3 Multiplying Matrices Objectives 1 Multiply matrices
4 -3 Multiplying Matrices Objectives: 1. Multiply matrices. 2. Use the properties of matrix multiplication.
Multiplying Matrices �You can multiply two matrices if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. �When you multiplying two matrices Amxn and Bnxr, the resulting matrix AB is an m x r matrix.
Dimensions of Matrix Products �Determine whether each matrix product is defined. If so, state the dimensions of the product. �Example: A 4 x 6 and B 6 x 2
Dimensions of Matrix Products �Determine whether each matrix product is defined. If so, state the dimensions of the product. �Example: A 4 x 6 and B 6 x 2 �Answer: 4 x 2
Dimensions of Matrix Products �Determine whether each matrix product is defined. If so, state the dimensions of the product. �Example: A 4 x 6 and B 6 x 2 �Answer: 4 x 2 �Example: A 3 x 4 and B 4 x 2
Dimensions of Matrix Products �Determine whether each matrix product is defined. If so, state the dimensions of the product. �Example: A 4 x 6 and B 6 x 2 �Answer: 4 x 2 �Example: A 3 x 4 and B 4 x 2 �Answer: 3 x 2
Dimensions of Matrix Products �Determine whether each matrix product is defined. If so, state the dimensions of the product. �Example: A 3 x 2 and B 3 x 2
Dimensions of Matrix Products �Determine whether each matrix product is defined. If so, state the dimensions of the product. �Example: A 3 x 2 and B 3 x 2 �Answer: The matrix is not defined.
Dimensions of Matrix Products �Determine whether each matrix product is defined. If so, state the dimensions of the product. �Example: A 3 x 2 and B 3 x 2 �Answer: The matrix is not defined. �Example: A 3 x 2 and B 4 x 3
Dimensions of Matrix Products �Determine whether each matrix product is defined. If so, state the dimensions of the product. �Example: A 3 x 2 and B 3 x 2 �Answer: The matrix is not defined. �Example: A 3 x 2 and B 4 x 3 �Answer: The matrix is not defined.
Multiplying Matrices �Find RS if
Multiplying Matrices �Find RS if
Multiplying Matrices �Find RS if (first row, first column)
Multiplying Matrices �Find RS if (first row, second column)
Multiplying Matrices �Find RS if (second row, first column)
Multiplying Matrices �Find RS if (second row, second column)
Multiplying Matrices �Find UV if
Multiplying Matrices �Find UV if
Multiplying Matrices �Find UV if
Multiplying Matrices �Find UV if
Multiplying Matrices �Find UV if
Properties of Multiplying Matrices �Matrix multiplication is NOT commutative. �This means that if A and B are matrices, AB≠BA.
AB≠BA in Matrices �Find KL if
AB≠BA in Matrices �Find KL if
AB≠BA in Matrices �Find KL if
AB≠BA in Matrices �Find KL if
AB≠BA in Matrices �Find KL if
AB≠BA in Matrices �Find LK if
AB≠BA in Matrices �Find LK if
AB≠BA in Matrices �Find LK if
AB≠BA in Matrices �Find LK if
AB≠BA in Matrices �As you can see, multiplication is NOT commutative. �The order of multiplication matters.
Properties of Multiplying Matrices Distributive Property �If A, B, and C are matrices, then �A(B+C)=AB+AC and �(B+C)A=BA+CA
Distributive Property �Find A(B+C) if
Distributive Property �Find A(B+C) if
Distributive Property �Find A(B+C) if
Distributive Property �Find A(B+C) if
Distributive Property �Find A(B+C) if
Distributive Property �Find A(B+C) if
Distributive Property �Find A(B+C) if
Distributive Property �Find AB+AC if
Distributive Property �Find AB+AC if
Distributive Property �Find AB+AC if
Distributive Property �Find AB+AC if
Distributive Property �Find AB+AC if
Distributive Property �Find AB+AC if
Distributive Property �Find AB+AC if
Distributive Property �As you can see, you can extend the distributive property to matrices.
- Slides: 48
![Multiply a=[[0,4],[0,8]]](https://slidetodoc.com/wp-content/uploads/2020/11/2007532_5e6f092a8756a8c820c7677eaddb280b-300x225.jpg "Multiply a=[[0,4],[0,8]]")
