Determinant of a matrix
From Determinants.
From Determinants.
Diagonalizability.
Diagonalizability.
Diagonalizability.
The material is from Diagonalizability.
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. 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?
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...
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...
Please kindly show each step of your solution. Thank you. Without using Proposition 2.9, show that for any elementary matrix E...
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.
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.
Please see attached. Prove that the roots of the characteristic equation of A(L) are...
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 )
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), ...}.
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?
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.
2. the perimeter of a rectangle is 26m. the length is 1 m more than twice the width. Find the dimensions What is the length? _____m what is the with?______m 4. Solve by the elimination method x+5y=34 -x+9y=50 5.Solve by the elimination method 5x+5y= -13 -------------(1) 7x-3y= 19 -------------(2) 16. Solv
I am struggling with this transformation problem. Please include all steps and justifications. See attached file for full problem.
Solve the system of equations by graphing ... Solve by the substitution method ... See the attached file.
Linear Growth: Suppose that the amount that your town's population grows each year is fixed (or constant). Choose the amount of population growth each year =
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?
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
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.
Please see attached file
Please see attached file.
MTH212 Unit 3 - Individual Project A 1. To raise money, the local baseball teams decided to sell team logo hats (H) and T-shirts (T). The league director decided to hold a contest among the teams to see which team can raise the most money. The contest lasted for 3 weeks. Here are the results of the first 2 weeks. The numbers
Please help with the attached problems.
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
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}.