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Section 10.2.1 – Operations with Matrices

Section 10.2.1 – Operations with Matrices. No Calculator. 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. Addition of Matrices.

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Section 10.2.1 – Operations with Matrices

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  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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