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    Linear Algebra

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    Linear Algebra

    The characteristic polynomial. If you have any question or suggestion, please let me know.

    A stamp collection consists of 3, 8, and 15 cent stamps.

    A stamp collection consists of 3, 8, and 15 cent stamps. The number of 8 cent stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less than the number of 8 cent stamps. The total value of all the stamps is $2.47. Find the number of 8 cent stamps in the collection?

    Linear Algebra - Cofactors and Cramer's Rule

    Please see the attached file. Please kindly show each step of your solution. Thank you. Given three such points, show that the equations of a parabola and a circle are, respectively...

    Determinant Function Proof

    Please see the attached file. Please kindly show each step of your solution. Without using Proposition 2.6, prove that the determinant function is uniquely determined by the properties listed...

    Prove the system equations if A is a 2 x 2 matrix with integer entries.

    4. Let A be a 2 x 2 matrix with integer entries. Prove that the system of equations (a_11)(x_1) + (a_12)(x_2) = b_1 (a_21)(x_1) + (a_22)(x_2) = b_2 has a solution with x_1 and x_2 integers for all integers b_1 and b_2 if and only if D(A_1, A_2) = +/- 1. Interpret this result geometrically.

    Show that the Inverse Matris has All Integer Entries

    3. Let A be a 2 x 2 matrix with integer entries. a. Suppose D(A_1, A_2) = +/- 1. Show that A^-1 has all integer entries. *b. Conversely, suppose A and A^-1 are both matrices with integer entries. Prove that D(A_1, A_2) = +/- 1.

    Determinants, Matrices, Inverse, Linear equations

    Practice problems on determinants and matrices. All questions can be found in the attached file. Write the matrix equation as a system of equations and solve the system. ■(1&2&3@1&1&1@-1&1&2) {█(x@y@z)┤ = {█(1@12@2)┤ Find the determinant of the given matrix. ■(1&0&6 -1@-6&0&2 4@3&0&6 -2 )

    Description of Equivalence Relations

    Describe the equivalence relation on each of the following sets with the given partition. (a) Z, {..., {-2}, {-1}, {0}, {1}, {2}. {3, 4, 5, ...}}. (b) R, {(- infinity, 0), {0}, (0, infinity)}. (c) R, {..., (-3, -2,), {-2}, (-2, -1), {-1}, (-1, 0), {0}, (0,1), {1}, (1, 2), {2}, (2, 3), ...}.

    Landscape Design, Buying a Home and Fueling up

    Questions 1. Exercise: Four Concept Check Post your 50 word response to the following: Explain in your own words why the line x = 4 is a vertical line. 2. DQ 5-1 Post your response to the following: What similarities and differences do you see between functions and linear equations? Are all linear equations functions?

    Linear Equations and Linear Inequalities

    In what fundamental way does the solution set of a system of linear equations differ from the solution set of a system of linear inequalities? Give examples. Discuss the important implications arising from this difference.

    Solving a System of Linear Equations

    Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? What circumstances would cause you to use a different method?

    MTH 212: Unit 4 Group Project - A

    Can you help solve the attached file? 1. Along a straight shoreline, two lighthouses, A and B, are located 2000 feet apart. A buoy lies in view of both lighthouses, with angles 1, 2, and 3 as indicated. (Angle 1 is denoted by , angle 2 is denoted by , and angle 3 is denoted by .) A. By looking at the picture, do you th

    Constructing an orthonormal basis

    V1=(0.6, -0.8, blank), v2=(blank, blank, 1), v3=(blank,-0.6,blank) Find the values of the blanks that make these vectors an orthonormal basis for R^3. The attachment contains the question formulated with correct mathematical notation.

    Systems of equations points

    Either substitution or elimination to find the locus of points that satisfy both equations 3y = 2 - x 2x = 7 - 3y y = 2x + 1 y = 4x + 7 3x + 2y = 10 6x - 3y = 6

    Linear Algebra : Linear Transformations and Standard Basis

    Please see the attached file. Please show each step of your solution. Thank you. Define T: P_3 -> P_3 by T(f)(t) = 2f(t) + (1 - t)integral'(t). a. Show that T is a linear transformation. b. Give the matrix representing T with respect to the "standard basis" {1, t, t^2, t^3}.