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    In-Class Assignment 1

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    Hướng Dương Lê Vũ
    1) The document provides an in-class assignment on linear algebra with 4 questions. 2) The first question asks students to identify which of 4 equations are linear equations in variables x1, x2, and x3. 3) The second question asks students to write out the systems of linear equations corresponding to 4 augmented matrices and solve them. 4) The third question asks students to solve 3 systems of linear equations using Gaussian elimination, showing the row operations. 5) The final question asks students to determine the values of a for which a system will have no solutions, exactly one solution, or infinitely many solutions.

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    In-Class Assignment 1

    Uploaded by

    Hướng Dương Lê Vũ
    32 views3 pages
    1) The document provides an in-class assignment on linear algebra with 4 questions. 2) The first question asks students to identify which of 4 equations are linear equations in variables x1, x2, and x3. 3) The second question asks students to write out the systems of linear equations corresponding to 4 augmented matrices and solve them. 4) The third question asks students to solve 3 systems of linear equations using Gaussian elimination, showing the row operations. 5) The final question asks students to determine the values of a for which a system will have no solutions, exactly one solution, or infinitely many solutions.

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    1) The document provides an in-class assignment on linear algebra with 4 questions. 2) The first question asks students to identify which of 4 equations are linear equations in variables x1, x2, and x3. 3) The second question asks students to write out the systems of linear equations corresponding to 4 augmented matrices and solve them. 4) The third question asks students to solve 3 systems of linear equations using Gaussian elimination, showing the row operations. 5) The final question asks students to determine the values of a for which a system will have no solutions, exactly one solution, or infinitely many solutions.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    32 views3 pages

    In-Class Assignment 1

    Uploaded by

    Hướng Dương Lê Vũ
    1) The document provides an in-class assignment on linear algebra with 4 questions. 2) The first question asks students to identify which of 4 equations are linear equations in variables x1, x2, and x3. 3) The second question asks students to write out the systems of linear equations corresponding to 4 augmented matrices and solve them. 4) The third question asks students to solve 3 systems of linear equations using Gaussian elimination, showing the row operations. 5) The final question asks students to determine the values of a for which a system will have no solutions, exactly one solution, or infinitely many solutions.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    Linear Algebra

    Instructor: Le Hai Yen


    In-Class Assignment 1 October 25, 2022

    Students:

    Recall: Common method to solve a linear system using Gaussian/Gauss-Jordan elimination:

    1) Construct a matrix (called the augmented matrix) corresponding to the system

    2) Using elementary row operations on matrices to reduce the augmented matrix to an upper triangular
    matrix.
    3) Using back-substitution to solve the final system.

    Question 1. Which of the following are linear equations in x1 , x2 and x3 ?


    √ √
    1. x1 + 5x2 − x3 = 1 3. πx1 − 2x2 + 31 x3 = 71/3
    √ √
    2. x−2
    1 + x2 + 8x3 = 5 4. x1 − 3x2 + 4−√
    5
    32
    x3 = 2

    Question 2. The following matrices are the augmented matrices of systems of linear equations in variables
    x1 , x2 , . . .. Write down the corresponding systems explicitly and solve them.

    1. 2. 3. 4.
     
        1 6 0 0 4 −2  
    1 0 0 5 1 0 0 4 −1 0
     0 1 0 3 1 1 2 0 3 0 7
    0 1 0 −2 0 1 0 2 6  0 0 0 1 5 2 0 0 1 0 0 1
    0 0 1 4 0 0 1 3 2 0 0 0 0 0 0 0 0 0 0 1 2
    Linear Algebra
    Instructor: Le Hai Yen
    In-Class Assignment 1 October 25, 2022

    Question 3. Solve the following linear systems using Gaussian or Gauss-Jordan (back-substitution) elimination.
    Write clearly all elementary row operations you used.

    1. 2. 3.

    x + y + 2z = 0 2x + 2y + 2z = 0 x + 2y − t + w = 1
    2x + 4y − 3z = 1 −2x + 5y + 2z = 1 3y + z − w = 2
    3x + 6y − 5z = 0. 8x + y + 4z = −1. z + 7t = 1.
    Linear Algebra
    Instructor: Le Hai Yen
    In-Class Assignment 1 October 25, 2022

    Question 4. For which values of a will the following system have no solutions? Exactly one solution? Infinitely
    many solutions?

    x + 2y − 3z = 4
    3x − y + 5z = 2
    4x + y + (a2 − 14)z = a + 2.

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