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# 4-3 Multiplying Matrices - PowerPoint PPT Presentation

4-3 Multiplying Matrices. Objectives: Multiply matrices. 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.

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### 4-3 Multiplying Matrices

Objectives:

Multiply matrices.

Use the properties of matrix multiplication.

• 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.

• Determine whether each matrix product is defined. If so, state the dimensions of the product.

• Example: A4x6 and B6x2

• Determine whether each matrix product is defined. If so, state the dimensions of the product.

• Example: A4x6 and B6x2

• Answer: 4x2

• Determine whether each matrix product is defined. If so, state the dimensions of the product.

• Example: A4x6 and B6x2

• Answer: 4x2

• Example: A3x4 and B4x2

• Determine whether each matrix product is defined. If so, state the dimensions of the product.

• Example: A4x6 and B6x2

• Answer: 4x2

• Example: A3x4 and B4x2

• Answer: 3x2

• Determine whether each matrix product is defined. If so, state the dimensions of the product.

• Example: A3x2 and B3x2

• Determine whether each matrix product is defined. If so, state the dimensions of the product.

• Example: A3x2 and B3x2

• Answer: The matrix is not defined.

• Determine whether each matrix product is defined. If so, state the dimensions of the product.

• Example: A3x2 and B3x2

• Answer: The matrix is not defined.

• Example: A3x2 and B4x3

• Determine whether each matrix product is defined. If so, state the dimensions of the product.

• Example: A3x2 and B3x2

• Answer: The matrix is not defined.

• Example: A3x2 and B4x3

• Answer: The matrix is not defined.

• Find RS if

• Find RS if

• Find RS if

(first row, first column)

• Find RS if

(first row, second column)

• Find RS if

(second row, first column)

• Find RS if

(second row, second column)

• Find UV if

• Find UV if

• Find UV if

• Find UV if

• Find UV if

• 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.

Distributive Property

• If A, B, and C are matrices, then

• A(B+C)=AB+AC and

• (B+C)A=BA+CA

• Find A(B+C) if

• Find A(B+C) if

• Find A(B+C) if

• Find A(B+C) if

• Find A(B+C) if

• Find A(B+C) if

• Find A(B+C) if

• Find AB+AC if

• Find AB+AC if

• Find AB+AC if

• Find AB+AC if

• Find AB+AC if

• Find AB+AC if

• Find AB+AC if

• As you can see, you can extend the distributive property to matrices.