| A) Structure | |
|---|---|
| I) Definition | |
| 1) Identifying the Size of a Matrix | Ex 1 Ex 2 Ex 3 Ex 4 |
| 2) Identifying the Entries of a Matrix | Ex 5 Ex 6 Ex 7 Ex 8 |
| II) Special Matrices | |
| 3) Identifying Types of Matrices | Ex 9 Ex 10 Ex 11 Ex 12 Ex 13 Ex 14 |
| 4) Constructing Special Matrices | Ex 15 Ex 16 Ex 17 |
| III) Equality | |
| 5) Identifying Equal Matrices | Ex 18 Ex 19 Ex 20 |
| 6) Solving for Unknowns Using Matrix Equality | Ex 21 Ex 22 Ex 23 |
| B) Matrix Operations | |
| I) Matrix Addition | |
| 7) Verifying the Condition for Addition | Ex 24 Ex 25 Ex 26 |
| 8) Calculating Matrix Sums | Ex 27 Ex 28 Ex 29 Ex 30 |
| 9) Calculating Matrix Differences | Ex 31 Ex 32 Ex 33 |
| 10) Evaluating Matrix Expressions | Ex 34 Ex 35 Ex 36 Ex 37 |
| 11) Proving the Properties of Addition | Ex 38 Ex 39 Ex 40 |
| II) Scalar Multiplication | |
| 12) Calculating Scalar Products | Ex 41 Ex 42 Ex 43 Ex 44 |
| 13) Evaluating Matrix Expressions | Ex 45 Ex 46 Ex 47 Ex 48 |
| 14) Simplifying Matrix Expressions | Ex 49 Ex 50 Ex 51 Ex 52 |
| III) Matrix Multiplication | |
| 15) Verifying the Condition for Multiplication | Ex 53 Ex 54 Ex 55 |
| 16) Determining the Size of the Product | Ex 56 Ex 57 Ex 58 |
| 17) Calculating Matrix Products | Ex 59 Ex 60 Ex 61 Ex 62 Ex 63 Ex 64 |
| 18) Investigating Commutativity | Ex 65 Ex 66 Ex 67 |
| 19) Expanding Matrix Expressions | Ex 68 Ex 69 Ex 70 Ex 71 |
| 20) Simplifying Powers of a Matrix | Ex 72 Ex 73 Ex 74 |
| C) Invertible Matrices | |
| I) Definition | |
| 21) Verifying an Inverse by Definition | Ex 75 Ex 76 Ex 77 |
| 22) Proving Properties of the Inverse | Ex 78 Ex 79 Ex 80 Ex 81 |
| II) Finding the Inverse of a 2x2 Matrix | |
| 23) Calculating the Determinant | Ex 82 Ex 83 Ex 84 |
| 24) Finding the Inverse of a 2x2 Matrix | Ex 85 Ex 86 Ex 87 Ex 88 Ex 89 |
| 25) Finding the Condition for Invertibility | Ex 90 Ex 91 Ex 92 Ex 93 |
| D) Applications | |
| I) Solving Systems of Linear Equations | |
| 26) Writing a System in Matrix Form | Ex 94 Ex 95 Ex 96 |
| 27) Solving Systems with the Inverse Method | Ex 97 Ex 98 Ex 99 |