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Linear Algebra

System of Equation Word Problems

Please see the attached document for better formatting: _____________________________________________________ Review examples 2, 3, and 4 in section 8.4 of the text. How does the author determine what the first equation should be? What about the second equation? How are these examples similar? How are they different? P

Solving systems of equations

3.) Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent. 5u+v=9 5u=v+21 What is the solution of the system of equations? ____________________ (Type an ordered pair . Type N if there is no solution. Type R if the solution is a

Linear Equations In Real World

I need to show a linear equation and explain what it represents. I need to state what the "x" and "Y" in equation represents I have to be able to evaluate the equation for at least two variables and provide reference where you got the equation from. Part 2: Using the Library, web resources, and/or other materials, find a r

Judy and Pete are building a new house and want to carpet their living room

Please see the attached file. 1. Judy and Pete are building a new house and want to carpet their living room, except for the entrance way and the semicircle in front of the fireplace that they want to tile (Alexander & Koeberlein, 2003). A. How many square yards of carpeting are needed? (Hint: There are 9 square feet

LINEAR ALGEBRA

1. Let a1, a2, a3 be linearly independent vectors in R3, and let A = [a1 a2 a3]. Which of the following statements are true? a) The reduced row echelon form of A is I3 b) The rank of A is 3 c) The system [A|b] has a unique solution for any vector b in R3 d) (a), (b) and (c) are all true e) (a) and (b) are both true, but not

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 - Determinants

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

Linear Algebra - Determinants

Please kindly show each step of your solution. Thank you. Without using Proposition 2.9, show that for any elementary matrix E...

Linear Algebra - Signed Area and Matrix 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.

Linear Algebra - Signed Area and Matrix 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.

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.

Linear Algebra : Orthogonality

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.

Equations

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 - Rotations

Please see the attached file for the fully formatted problems. Calculate the standard matrix for each of the following linear transformations T. a. T: R^2 -> R^2 given by rotating -pi/4 counterclockwise about the origin and then reflecting across the line x_1 - x_2 = 0. b. T: R^3 -> R^3 given by rotating pi/2 counterclo

Linear Algebra - Basis and Dimension

Please see the attached file. Please show each step of your solution. Thank you. Find a basis for each of the given subspaces and determine its dimension. V = Span ((1, 2, 3), (3, 4, 7), (5, -2, 3)) C R^3