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Understanding Matrix Operations: Addition, Subtraction, and Multiplication Basics

This section covers essential matrix operations without a calculator, focusing on matrix addition, subtraction, and scalar multiplication. It emphasizes the requirement that matrices must have the same dimensions for addition and subtraction to be valid. The critical distinctions of matrix multiplication are highlighted, including the importance of order and dimension compatibility. Step-by-step instructions for performing matrix multiplication are provided, ensuring clarity around determining the feasibility of operations and calculating the resulting dimensions.

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Understanding Matrix Operations: Addition, Subtraction, and Multiplication Basics

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Presentation Transcript

  1. Section 10.2.1 – Operations with Matrices No Calculator

  2. Matrix – an array (set) of numbers arranged in rows and columns Dimension of a Matrix – number of rows x number of columns 2 x 2 3 x 2 4 x 1 1 x 1 1 x 3 2 x 3

  3. Addition of Matrices Dimensions MUST be the same for sum to exist Sum - DNE Sum - DNE

  4. Subtraction of Matrices Dimensions MUST be the same for sum to exist Sum - DNE Sum - DNE

  5. Scalar – a number SCALAR Multiplication (always works)

  6. MATRIX MULTIPLICATION • Order makes a difference…AB is different from BA • Number of columns in first matrix must equal number of • rows in second matrix. (middle numbers match) • Answer will be number of rows in first matrix by number of • columns in second matrix. (outside numbers) Are the following matrix multiplications possible? 2 x 1 1 x 2 2 x 1 1 x 2

  7. YES NO YES YES 3 x 23 x 2 3 x 22 x 3 3 x 11 x 3 2 x 33 x 2 YES NO 2 x 22 x 2 3 x 3 2 x 2 Are the following matrix multiplications possible?

  8. YES YES NO YES 3 x 23 x 2 3 x 22 x 3 3 x 11 x 3 2 x 33 x 2 YES NO 2 x 22 x 2 3 x 3 2 x 2 What is the dimension of the answer going to be? 2 x 2 3 x 3 3 x 3 2 x 2

  9. MATRIX MULTIPLICATION STEPS 1. Is the multiplication possible? (middle numbers match) 2. If yes, what is the dimension of the answer? (outside numbers) 3. Create “blank” matrix. 4. “Multiply/Add” corresponding rows and columns

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