Matrices and explanations and detailed working for solving system of linear equations using matrix method. These solutions contain finding invese matrix, transpose of matrix, determinant of matrix and other operations.

1. solve the following equations and show work. 2. You are given the following system of linear equations: x – y + 2z = 13 2x + xy – z = -6 -x + 3y + z = -7 a. Provide a coefficient matrix corresponding to the system of linear equations. b. What is the inverse of this matrix? c. What is the transpose of this mat ...continues

Matrices with no solutions and infinite solutions

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 ...continues

Matrix Reflection and Rotation

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 orthoganal 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/( ...continues

Matrix Reflection and Rotation

Matrix reflection and rotation Given the 3x3 matrices A and B (active transformation matrices) do the following: (A, B are 3x3 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. ...continues

Subsets, Projection Maps, Basis and Direct Sums

Let n >= 1. Define the subsets U and W in V = F^n as follows: U = {(x_1, . . . , x_n) : x_1 + . . . + x_n = 0} W = {(x_1, . . . , x_n) : x_1 = . . . = x_n} a) Prove that U and V are subspaces of V . b) Prove that V = is the "direct sum" of U and W. c) Let (v_1, . . . v_n) = ((1, 0, . . . , 0), (0, 1, . . . , 0), . . . , ...continues

Eigenvectors and Eigenvalues

Assume that ST = TS. Prove that the operators S and T have a common eigenvector. Let V be a complex (i.e. F = R) finite dimensional vector space. Let S, T be elements of L(V ) (set of operators on V). Assume that ST = TS. Prove that the operators S and T have a common eigenvector. these are the steps: a) Explain why T ...continues

Complex n-tuples, Basis and Diagonalization

Let T be an element of L(C^3) [complex 3-tuples] be the operator defined by T(z_1, z_2, z_3) = (z_2, z_3, z_1). a) Write the matrix of T in the standard basis of C^3. b Find all eigenvalues of T c) Is there a basis of C^3 such that the matrix of T in that basis is diagonal? If your answer is ”NO”, explain why. If your ...continues

Linear Operators : Finite dimensional Space and Nullity

Let V be a finite-dimensional real (i.e. F = R) vector space. Let T be an element of L(V)(set of operators on V), and assume that T^2 = 0. a) Prove that rangeT is contained in nullT. b) Prove that dimnullT >= (dimV )/2. Hint. Make use of a)

Graphing and Functions

1. Suppose I had a lemonade stand. When I charge $1, I sold 50 cups, when I raised the price to $2, I only sold 25 cups. Write an equation for the number of cups I sold as a function of the price i charged. Denote C for number of cups and P for price. Assume the function is linear. 2. Write an equation for f(x) based on x -2, ...continues

Linear functions: Real Life Examples

Think of 2 functions that represent something from your life. for example the # of beers you drink depends on the # of football games you watch, if you drink 5 beers per game the function would be # for beers (b)= 5 times # of football games (f) or b=5F. Please write a brief paper describing of a linear equation that comes fr ...continues