• HW for 5/21

    Posted by Allen Olsen on 5/21/2018

    Objective: Finish up Gaussian Elimination and Systems of Equations over the next few days, for a quiz on Friday 5/25 (C, D) or Tuesday 5/29 (A).

    HW: To prepare for the Quiz, you must have completed

    1. The 2 by 2 Gaussian Elimination (by hand) handout.

    2. The 3 by 3 Gaussian Elimination using Matrices (by hand) handout.

    You were supposed to complete both of these handouts on the weekend.

    3. The new Solving Systems by Calculator handout, from today.  This shows you how to do Gaussian elimination on a matrix using the rref() function on your calculator.  rref() stands for "Reduced Row Echelon Form."

    4. The Linear Systems Applications handout, which you should start on once you get done with the previous handouts, and which I will hand out in your next class.

     

    Let me know if you have any trouble downloading these.

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  • HW for 5/18 (A, C, D)

    Posted by Allen Olsen on 5/18/2018

    Objective: Solve 2 by 2 and 3 by 3 systems of equations using the method of Gaussian Elimination.

    HW: 

    First, this handout, which is a short summary of the 2 by 2 case and then, on the last page, has some problems for you to do.

    This handout -- the first three pages are summaries of what we have done with 3 by 3 elimination, and the last page (page 4) has a problem to do and the rest of the HW assignment.

     

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  • Posting for 5/15 (A, D), 5/16 (C)

    Posted by Allen Olsen on 5/15/2018

    Objective: Multiply matrices!

    We worked through examples in class of how to do the matrix problems I assigned.  Some of you had difficulties downloading the homework.  Try this link, instead. 

    Tonight, please get all the way through these problems.

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  • HW for 5/14

    Posted by Allen Olsen on 5/14/2018

    Objective: Define matrices and use matrix multiplication to solve problems involving linear transformations.

    Here is a summary of the rules and justification of the rules for matrix multiplication.

    HW: This set of problems.

    If you had trouble with the second link, try this.

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  • HW for 5/9

    Posted by Allen Olsen on 5/9/2018

    Objective: Finish preparing for the quiz on Thursday (A) or Friday (C, D).

    The sample problems handout is here.  You should finish it before taking the exam.

    Today I handed out solutions in class, but they are not yet available in electronic form.

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  • HW for 5/7

    Posted by Allen Olsen on 5/7/2018

    1. Rework the 3 x 3 systems of equations assigned on 5/2, using the elimination method instead of the substitution method.  Consult the solutions I handed out in class as models for how to do this.

    2. Solve the 2 x 2 systems of equations assigned on 5/1, using Cramer's Rule, as explained in class.

    3. In the next class, we will be proving the following 3 x 3 Cramer's Rule: 3 x 3 Cramer's Rule.

    Consider how this could be applied to solve one of the 3 x 3 systems of equations.  There are now three variables, whose values are the ratios of two determinants.  See if you can figure out what the generalization of Cramer's Rule is from 2 x 2 systems to 3 x 3 systems.  What numbers would go into the determinant that is in the denominator?  What numbers would go into the determinant that is the x-numerator?  The y-numerator?  The z-numerator?

     

    Quiz announcement:  There will be a quiz Thursday - Friday this week in class covering the work we have done with vectors and the work done with systems of equations so far. Specifically: A Block will take the quiz on Thursday; C and D Blocks will take it on Friday.

    Some of you will be unable to take the quiz as scheduled because of AP exams or other commitments that do not allow you to be in class on that date.  If you are unable to take the test on Thursday, you must let me know in advance and make other arrangements to take the quiz this week.  For example, if you have APUSH on Friday, you could take the quiz Thursday after school, or in an I-block, etc.  If you are scheduled to take it Thursday but won't be in class, then you could take it Friday instead.

    To start preparing for this, make sure that you have completed the homework problems for this unit (see the web site).  I will hand out a set of sample questions for the quiz in the next class. 

     

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  • HW for 5/4 (C, D)

    Posted by Allen Olsen on 5/4/2018

    Objective: Solve 3 by 3 systems of equations using the elimination method. 

    HW: Using the solution set handed out in class, complete the 16 assigned problems.  You are trying to pick a method that reduces the amount of arithmetic needed to get a solution.

    Additional HW for D Block: On page 526, solve 3 - 12, 19 - 22 (2 by 2 systems) using determinants.

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  • HW for 5/2 (A, D), 5/3 (C)

    Posted by Allen Olsen on 5/2/2018

    Objective: Solve three-by-three systems of equations using elimination.

    HW: This handout.  The solutions are below.

    1. a = a, b = -1, c = 2.

    2. x = 2, y = 3, z = -2.

    3. r = 1/2, s = 1/3, t = 4.

    4. m = -25, n = 18, p = -25.

    5. A = - 1/39, B = -16/13, C = -41/26.

    6. x = -15/61, y = -29/183, z = 2/61.

    7. x = 1, y = 2, z = 4.

    8. x = -1, y = 3, z = -2.

    9. x = 1/2, y = -1, z = -1/2.

    10. x = -2, y = 3, z = -3.

    11. x = 12, y = 8, z = 6.

    12. A = 2, B = 3/2, C = 21/4.

    13. R = 12, S = 8, T = -10.

    14. x = 2, y = -1, z = -2.

    15. x = 1/2, y = 1/3, z = -1/2.

    16. x = 1/6, y = 1/3, z = 1/2.

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  • HW for 5/1 (D, A), 5/2 (C)

    Posted by Allen Olsen on 5/1/2018

    Objective: Solve 2 by 2 and 3 by 3 systems of equations, using the methods of substitution, elimination, and Cramer's Rule.

    HW: Sect. 7.1, p. 526: problems 3 - 12, 19 - 22.

    Also, solve the following three systems of equations:

    1. x - 2y + z = 5                2. 3x + y - z = 11                     3. 2x + 3y - z = -1

       2x + y - z = -1                     x + 3y - z = 13                       3x        - 8z = -1

       3x + 3y - 2z = -4                 x + y - 3z = 11                               5y + 7z = -1

     

     

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  • HW for 4/30

    Posted by Allen Olsen on 4/30/2018

    Objective: Find the projection of one vector onto another.  Determine when two vectors are orthogonal.

    HW: Sect. 6.2, p. 473:

    problems 26, 28, 31, 32, 33 - 41 (odd), 58.

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