Matrices are the most common and popular way to solve systems of equations. Provide an example of a matrix that can be solved using Gaussian elimination. 1. Show specifically how row operations can be used to solve the matrix. 2. State the solution 3. substitute the solution back into the equation to verify the solution.
Please help me with the attached problems. I am totally lost when it comes to Matrices. 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
Please see the attached file for the fully formatted problem. Consider the field F_7 ~/= Z/7Z having 7 elements, and consider the matrix group: G= {(t s) |t E F(^x)(_7), x E F_7}. .......(0 t^(-1)) Find all Sylow 3-subgroups of G. Can you find a "systematic" way of describing them?
If an art dealer sold two artworks for $1520.00 thereby making a profit of 25% on the first piece of art and 10% on the second piece, if he had approached any exhibition he would have sold them together for $1535.00 with a profit of 10% on the first piece and 25% on the second, find the actual cost of each piece?
Please see the attached file for the fully formatted problems.
Given the 2x2 matrices A, B, and C (active transformation matrices) in the x, y plane do the following: (A, B and C are 2x2 matrices given below) 1. Show the matrix is orthogonal 2. Find the determinant to indicate if a rotation or reflection matrix 3. Find the rotation angle or find the line of reflection. A= 1/(2)
Provide an example of a matrix that has no solution. Use row operations to show why it has no unique solution. Also, some matrices have more than one solution (in fact, an infinite number of solutions) because the system is undetermined. (In other words, there are not enough constraints to provide a unique solution.) Provide an
Find all invertible matrices A of the form A =[a b] [c d] and satisfying A = A−1 and A^T = A^−1. Hint: The identity cos^2 t + sin^2 t = 1 may be useful.
Consider a circle with radius 1. The vectors OP and OQ shown in the diagram below are the unit vectors i and j rotated by angle t respectively.
Let G be a graph with p vertices and p-1 edges. Prove that G is a tree iff any p-1 rows of the incidence matrix are linearly independent over Z/(2) (integers modulo 2).
Let B, C, D, E, F and G be the following matrices: 1 3 2 6 3 9 1 -1 0 0 2 3 0 0 2 1 -1 0 0 1 1 1 0 1 2 1 0 0 0 0 -1 -1 0 0 0 3 0 0 0 0 1 1 3 4 4 6 -2 -3 I would welcome an explanation of whether: - the columns of each matrix are independent - the rows of each matrix are independent
Let A be the following (2x3) matrix: 1 0 2 2 1 3 I would welcome an explanation of whether: - the columns of A are independent - the rows of A are independent - the columns of A span R2 or R3 - the rows of A span R3 - the rank of A is 1 or 2.
Please see the attached file for the fully formatted problems. MTH212 Unit 3 - Individual Project B 1. Five neighborhoods (NB) all want to raise money for a playground for their kids. The neighborhood that raises the most money will be able to choose the name of the park. To raise money, they all decide to have a bake sale
Need help making a matrix into a word problem. See attached file for full problem description. From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be creative. Do not use
Animal Growth - At the beginning of a laboratory experiment, five baby rats measured. 5.6,6.4,6.9,7.6, and 6.1cm in length, and weighed 144, 138, 149, 152 and 146g, respectively. a). Write a 2*5 matrix using this information b). At the end of two weeks, their lengths ( in centimeters) were 10.2, 11.4, 11.4, 12.7, and 10.8 and
Four friends (Gauss, Euler, Cramer, and Einstein) can solve a 20 variable system in 11 hours. Gauss, Euler and Cramer can do it in 18 hours, while Euler, Cramer and Einstein take 16 hours. Gauss, Euler and Einstein can do it together in 14 hours. Define variables, set up a system, and using matrices, determine how long it takes
If A and B are 3X3 matrices with Det(a)=2 and Det(b)=3 ... if possible evaluate the following expressions 1 Det(2AB) 2 Det(A^4 B^T a^-1) Where T is transpose and -1 is INVERSE
Let S= { (1, 2), (0, 1)} and T= { (1, 1), (2,3) } be bases for R^2 Let the Vector V=(1,5) and the vector W=(5,4) A. What are the coordinate vectors of V and W wrt to the basis T B. What is the transition matrix P from T to S basis? C. What are the coordinate vectors of V and W wrt to S (Using P from T to S basis)
With given Eigenvalues λ = 6, -2, 2, 1, - 7 and with given Eigenvectors 5 * 5 matrix given below respectively 1 0 1 2 -1 2 2 1 0 2 3 0 1 2 -3 4 3 1 0 4 5 1 1 3 -5 1) Find inverse power method on (A-1) 2) Shifted inverse power method on (A - CI)-1 Write Matlab script on both the methods.
Let A = {a, b, c) and R be the relation defined on A defined by the following matrix: M_R = (1 0 1) (1 1 0) (0 1 1) Describe R by listing the ordered pairs in R and draw the digraph of this relation.
Let: D = days of the week {M, T, W, R, F}, E = {Brian (B), Jim (J), Karen (K)} be the employees of a tutoring center at a University U = {Courses the tutoring center needs tutors for} = {Calculus I (I), Calculus II (II), Calculus III (III), Computers I (C1), Computers II (C2), Precalculus (P)}. We define the relation R
1. Solve the system of equations by using inverse matrix methods: 5x - y = 1 3x + y = 0 2. Find the determinant of matrix (should be brackets) -53 -96 9 2 Please see the attached file for the fully formatted problems.
Let N be an kxk matrix such that N^k=0 and N^(k-1) not equal to zero. Show that N and its transpose (N^t) are similar.
I am having problems with numbers 1-5 of the attached document. I understand numbers 6-10, but I can't seem to comprehend how to solve numbers 1-5.
Find a matrix of projection pi onto subspace V parallel to subspace W in R3. See attached file for full problem description.
Determine the solutions of the system of equations whose matrix is row-equivalent to: Give three examples of the solutions. Verify that your solutions satisfy the original system of equations.
Let A and B be arbitrary n x n matrices whose entries are real numbers. Use basic matrix laws only to expand (A + B)². Explain all steps. Hint: Use the distributive laws.
Compute: (a) AC + BC (It is much faster if you use the distributive law for matrices first.) (b) 2A - 3A See attached file for full problem description.
Find the inverse of |1 2 1| |1 1 2| |2 0 2|
Please see attached. A = [4 3; 0 1]; B = [1 0 2; 2 -1 0]; calculate A * B