1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Represent mathematical and real-world data in a matrix. Find sums and differences of matrices and the scalar product of a number and a matrix. 4.1 Using Matrices to Represent Data

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms additive inverse matrix dimensions of a matrix element entry image matrix pre-image scalar multiplication 4.1 Using Matrices to Represent Data

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Properties of Matrix Addition 4.1 Using Matrices to Represent Data CommutativeA + B = B + A Associative(A + B) + C = A + (B + C) Additive Inversematrix whose entries are opposites of those in a matrix Additive Identity m  n matrix with 0 as all of its entries A, B, C are matrices with dimensions m  n:

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Add and subtract matrices, and find the scalar product of a number and a matrix. 4.1 Using Matrices to Represent Data Step 1:scalar multiplication Find 4 2 –5 3 6 1 0 3 –2 1 2 3 – 1+ 4 4 2 –5 3 (–1)6 (–1)1 (–1)0 (–1)3 4(–2) 4(1) 4(2) 4(3) ++ 4 2 –5 3 –6 –1 0 –3 –8 4 8 12 ++

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Add and subtract matrices, and find the scalar product of a number and a matrix. 4.1 Using Matrices to Represent Data Step 2:addition and subtraction 4 2 –5 3 –6 –1 0 –3 –8 4 8 12 ++ 4 + (–6) 2 + (–1) –5 + 0 3+ (–3) –8 4 8 12 + –2 1 –5 0 –8 4 8 12 +

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Add and subtract matrices, and find the scalar product of a number and a matrix. 4.1 Using Matrices to Represent Data Step 3:addition and subtraction –2 1 –5 0 –8 4 8 12 + –2+ (–8) 1 + 4 –5 + 8 0 + 12 –10 5 3 12 TOC