- 1.1 (1/16)
- Terms: Linear equation, solution, system of linear equations, inconsistent, consistent, homogeneous, trivial solution, nontrivial solution, equivalent systems
- Examples: 1, 3, 5
- Problems: 1-21 [7, 15, 16]
- 1.2 (1/18)
- Terms: matrix, row, column, diagonal, aij, vector, matrix addition, (diagonal matrix, upper/lower triangular)
- Examples: 1
- Problems: 1-5, 12, 13 [5]
- 2.1 (1/18)
- Terms: elementary row operation, row equivalent, Gaussian elimination, back substitution
- Theorems: 2.1, 2.2, (2.3), (Cor 2.1), 2.4
- Examples: 3, 4, 7-12, 15, 16
- Problems: 5-9, 14-17, 29-31 [5, 7, 15, 29]
- 1.3 (1/23)
- Terms: dot product, (transpose), matrix multiplication, Ax=b
- Examples: 1, 2, 4-11, 14, 15
- Problems:
- 1.4 (1/23)
- Terms: zero matrix, (identity matrix)
- Theorems: 1.1, 1.2, 1.3, 1.4
- Examples: 1-9
- Problems:
- 1.6 (1/25)
- Terms: matrix transformation, image, range, reflection, projection, dilation, contraction
- Examples: 1-6, 8
- Problems: 1-17, 20-22 [9, 21]
- 5.1 (1/30)
- Terms: linear transformation, linear operator, standard matrix representation
- Theorems: 5.1, 5.3
- Examples: 1-3, 10
- Problems: 5, 6, 8-11 [9, 11]
- 5.2 (2/1)
- Terms: one-to-one, kernel, range, image, onto
- Theorems: 5.4, Cor 5.1, 5.5
- Examples: 1-3, 5, 7ac
- Problems: 1, 2, 15 [2]
- 3.3 (2/1)
- Terms: subspace, closure, linear combination, span
- Theorems: 3.3, 3.4
- Examples: 1, 4, 5, 6, 7, 10
- Problems: 1-6, 19, 21-27 [6, 21, 19, 27]
- 3.4 (2/6)
- Terms: linearly (in)dependent
- Theorems: 3.5, 3.6
- Examples: 1, 3, 4, 6, 10
- Problems: 2, 7-10, 15, 16, 20-22 [2, 7, 15, 21]
- 3.5 (2/8)
- Terms: basis, standard basis, dimension
- Theorems: 3.7, 3.8, 3.9, Cor 3.1, Cor 3.2, Cor 3.3, Cor 3.4, Cor 3.5, 3.10, 3.11, 3.12
- Examples: 1, 3, 5, 7-10
- Problems: 1, 2, 7, 8, 11, 19, 20, 25, 26, 28, 33 [1, 7, 11, 19]
- 5.2 (2/13)
- Terms: nullity, rank
- Theorems: 5.6, Cor 5.2, 5.8
- Examples: 7, 8, 9
- Problems: 12, 15, 16, 21, 24-26, 29-31 [all of them]
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