Linear Algebra with Applications 2nd edition

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Jeffrey Holt
Publisher: W. H. Freeman

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  • Chapter 1: Systems of Linear Equations
    • 1.1: Lines and Linear Equations (25)
    • 1.2: Linear Systems and Matrices (40)
    • 1.3: Applications of Linear Systems (20)
    • 1.4: Numerical Solutions (15)
    • 1: Supplementary Exercises (21)

  • Chapter 2: Euclidean Space
    • 2.1: Vectors (32)
    • 2.2: Span (44)
    • 2.3: Linear Independence (41)
    • 2: Supplementary Exercises (22)

  • Chapter 3: Matrices
    • 3.1: Linear Transformations (18)
    • 3.2: Matrix Algebra (26)
    • 3.3: Inverses (24)
    • 3.4: LU Factorization (16)
    • 3.5: Markov Chains (16)
    • 3: Supplementary Exercises (26)

  • Chapter 4: Subspaces
    • 4.1: Introduction to Subspaces (33)
    • 4.2: Basis and Dimension (42)
    • 4.3: Row and Column Spaces (25)
    • 4.4: Change of Basis (16)
    • 4: Supplementary Exercises (20)

  • Chapter 5: Determinants
    • 5.1: The Determinant Function (41)
    • 5.2: Properties of the Determinant (30)
    • 5.3: Applications of the Determinant (29)
    • 5: Supplementary Exercises (19)

  • Chapter 6: Eigenvalues and Eigenvectors
    • 6.1: Eigenvalues and Eigenvectors (24)
    • 6.2: Diagonalization (13)
    • 6.3: Complex Eigenvalues and Eigenvectors (11)
    • 6.4: Systems of Differential Equations (19)
    • 6.5: Approximation Methods (17)
    • 6: Supplementary Exercises (18)

  • Chapter 7: Vector Spaces
    • 7.1: Vector Spaces and Subspaces (26)
    • 7.2: Span and Linear Independence (39)
    • 7.3: Basis and Dimension (24)
    • 7: Supplementary Exercises (14)

  • Chapter 8: Orthogonality
    • 8.1: Dot Products and Orthogonal Sets (19)
    • 8.2: Projection and the Gram–Schmidt Process (18)
    • 8.3: Diagonalizing Symmetric Matrices and QR Factorization (26)
    • 8.4: The Singular Value Decomposition (17)
    • 8.5: Least Squares Regression (20)
    • 8: Supplementary Exercises (22)

  • Chapter 9: Linear Transformations
    • 9.1: Definition and Properties (23)
    • 9.2: Isomorphisms (20)
    • 9.3: The Matrix of a Linear Transformation (38)
    • 9.4: Similarity (19)
    • 9: Supplementary Exercises (14)

  • Chapter 10: Inner Product Spaces
    • 10.1: Inner Products (39)
    • 10.2: The Gram–Schmidt Process Revisited (26)
    • 10.3: Applications of Inner Products (29)
    • 10: Supplementary Exercises (13)

  • Chapter 11: Additional Topics and Applications
    • 11.1: Quadratic Forms (23)
    • 11.2: Positive Definite Matrices (18)
    • 11.3: Constrained Optimization (18)
    • 11.4: Complex Vector Spaces (20)
    • 11.5: Hermitian Matrices (21)
    • 11: Supplementary Exercises (15)


Linear Algebra with Applications, 2nd edition, by Jeffrey Holt blends computational and conceptual topics throughout to prepare students for the rigors of conceptual thinking in an abstract setting. The early treatment of conceptual topics in the context of Euclidean space gives students more time, and a familiar setting, in which to absorb them. The WebAssign component for this title engages students with immediate feedback on end-of-chapter questions, detailed solutions, a Personal Study Plan, and links to a complete eBook.

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S - Supplementary Exercise
XP - Extra Problem


Question Availability Color Key
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Group Quantity Questions
Chapter 1: Systems of Linear Equations
1.S 21 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032 034 036 038 040 042
1.1 25 002 003 005 008 009 012 015 018 024 029 031b 037a 037b 038b 040 041 051a 051b 054a 055b 065 067 068 073 076
1.2 40 001 002 004 005 006 007 010 011 012 013 014 015 016 018 019 021 022 023 024 026 027 029 030 033b 034b 035a 043a 043b 044a 044b 045b 046a 046b 051 057 058 061 062 064 066
1.3 20 001 002 003 015 016 019 020 022 025 026 028 030 031 033 036 037 039 040 501.XP 502.XP
1.4 15 001 004 005 007 010 012 014 016 017 018 019 022 026 030 032
Chapter 2: Euclidean Space
2.S 22 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032 034 036 038 040 042 044
2.1 32 004 006 007 008 012 014 015 019 021 025 026 027 031 033 034 037 039 047 052 055 056 058 059 071b 072a 073a 073b 074b 075a 077a 078a 501.XP
2.2 44 002 004 007 008 010 011 013 014 016 017 018 020 021 022 023 024 025 026 028 029 030 031 032 035 037 047 048 049 050 059a 059b 060a 060b 061a 061b 062a 062b 063a 063b 064a 064b 065a 065b 079
2.3 41 002 003 004 005 007 008 009 010 011 013 014 016 017 019 020 021 022 023 024 026 028 033 034 043a 044a 047a 047b 048a 048b 049a 049b 050a 050b 051a 051b 052a 052b 066 067 072 073
Chapter 3: Matrices
3.S 26 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032 034 036 038 040 042 044 046 048 050 052
3.1 18 001 004 007 010 013 016 019 022 025 028 031 034 037 040a 046a 049 075 078
3.2 26 001 004 007 010 013 016 019 022 025 028 031 034 037 040 043 046 049 052a 058a 061a 079 082 085 088 501.XP 502.XP
3.3 24 003 006 009 012 015 018 021 024 027 030 033 036 039 043b 048a 051 054 059 071 074 077 080 083 086
3.4 16 003 006 009 012 015 018 021 025 028 031 034 037 040 043a 053 056
3.5 16 003 006 009 012 015 018 021 024 027 030 033a 036a 046 049 052 055
Chapter 4: Subspaces
4.S 20 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032 034 036 038 040
4.1 33 003 006 007 009 011 012 016 022 023 024 027 028 030 032 034 035 036 045a 045b 046a 046b 047a 047b 048a 048b 049a 051b 060 065 067 069 070 072
4.2 42 005 006 007 008 010 011 012 014 015 017 018 019 020 021 023 025 027 029 030 032 044a 044b 045a 045b 046a 046b 047a 047b 048a 048b 049a 049b 050a 050b 051 052 060 061 065 067 068 069
4.3 25 001 002 004 005 006 008 010 012 014 015 017 018 020 023 024 027 030 031 034 047a 048b 049a 051b 060 062
4.4 16 004 005 009 011 013 017 020 022 023 025 027 039a 040a 042a 042b 050
Chapter 5: Determinants
5.S 19 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032 034 036 038
5.1 41 001 002 003 004 005 007 008 010 012 013 014 016 019 022 023 025 028 030 031 034 035 037 039 042 045 048 050 051 053 056 057 069a 069b 070a 070b 071a 071b 072a 072b 077 080
5.2 30 002 003 004 005 007 008 009 011 015 017 020 022 024 027 028 033 035 036 040 047a 047b 048a 048b 049a 049b 050a 050b 051a 051b 069
5.3 29 001 002 004 008 012 013 015 017 020 022 023 025 027 030 031 032 033 035 041 043a 043b 044b 045a 045b 046b 059 062 063 066
Chapter 6: Eigenvalues and Eigenvectors
6.S 18 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032 034 036
6.1 24 002 004 006 008 009 010 011 014 015 018 023 024 025 026 037a 037b 039a 040a 040b 041a 047 067 501.XP 502.XP
6.2 13 003 006 007 009 010 012 013 015 019 032a 033b 034a 044
6.3 11 002 004 008 010 014 016 020 031b 034b 035b 036a
6.4 19 002 004 006 008 011 012 017 018 020 021 022 023 024 026 028 039a 040a 042 045
6.5 17 002 006 008 012 013 014 016 018 020 022 024 028 036a 037b 038b 044 051
Chapter 7: Vector Spaces
7.S 14 002 004 006 008 010 012 014 016 018 020 022 024 026 028
7.1 26 002 009 010 011 012 019 020 021 022 023 024 025 026 027 028 029 030 031 032 039b 040a 040b 041a 041b 042a 042b
7.2 39 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 033b 035a 035b 036a 036b 037a 037b 038a 051 052 053 054
7.3 24 001 002 003 004 005 006 007 008 009 010 011 012 025 026 030 038a 038b 039a 039b 040a 040b 041b 042a 042b
Chapter 8: Orthogonality
8.S 22 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032 034 036 038 040 042 044
8.1 19 002 004 005 006 008 010 012 015 018 019 026 031 035 037 049a 050a 052a 053b 071
8.2 18 001 003 004 006 008 010 011 013 016 018 021 024 026 029 038a 039a 039b 040b
8.3 26 003 005 006 011 012 014 016 017 019 021 023 029 031 033 034 036 038 049a 050a 051a 051b 052a 062 065 066 501.XP
8.4 17 002 005 008 010 012 013 016 018 022a 022b 023a 023b 024a 024b 026 037 039
8.5 20 001 003 005 007 009 011 013 021a 021b 022a 022b 023a 023b 031 035 038 039 043 048 052
Chapter 9: Linear Transformations
9.S 14 002 004 006 008 010 012 014 016 018 020 022 024 026 028
9.1 23 001 002 003 004 027 028 029 030 039a 039b 040a 040b 042a 042b 043a 043b 044a 045 046 061 062 063 064
9.2 20 011 012 013 015 016 017 018 022 031a 031b 032a 032b 033b 034b 036a 036b 037a 037b 038a 038b
9.3 38 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 041a 041b 043a 043b
9.4 19 001 003 004 005 006 009 010 011 013 014 015 016 017 019 025b 027a 027b 030a 038
Chapter 10: Inner Product Spaces
10.S 13 002 004 006 008 010 012 014 016 018 020 022 024 026
10.1 39 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 041a 041b 043b 044a 044b 045a 045b 046a 046b
10.2 26 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 025a 025b 026a 026b 027a 027b 028a 028b
10.3 29 001 002 003 004 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 029a 029b 030a 030b 032a 040 041 042 043
Chapter 11: Additional Topics and Applications
11.S 15 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030
11.1 23 001 002 003 006 008 010 011 012 013 014 016 018 019 020 022 023 024 026 035a 035b 037a 037b 038a
11.2 18 002 004 006 007 008 009 012 013 015 016 018 020 022 023 024 031a 033a 033b
11.3 18 002 004 005 006 008 010 012 013 014 016 017 018 019 021 022 023 031a 031b
11.4 20 002 003 006 007 008 009 011 012 014 017 019 021 023 028 030 037a 039a 039b 040a 040b
11.5 21 002 004 005 007 008 009 010 012 013 014 016 017 018 023a 023b 024a 024b 025a 025b 026a 026b
Total 1304