Value of Third-Order Determinants
Find the value of each of the third-order determinants:  2 0 -2   1 1 5  (this is a  3 4 5  3x3 matrix)
Matrices
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Matrices and equations
Protein, carbohydrates, and fats can be obtained from three foods. Each ounce of food I contains 5 grams of protein, 10 grams of carbohydrates, and 40 grams of fat. Each ounce of Food II contains 10 grams of protein, 5 grams of carbohydrates, and 30 grams of fat. Each ounce of Food III contains 15 grams of protein, 15 grams o
Matrix Representation: Orthogonal Transformation and Determinant
Please see the attached file for full problem description. Write a proof for the following statement: If P is an n x n orthogonal matrix, then det(P) = 1 or -1. Show work. Help: det: is the determinant
Matrix Representation : Orthogonal Transformation
Please see the attached file for full problem description. 1. Show that the 3 x 3 matrix P= [ 1/2 -1//2 0 ] [ 0 0 1 ] [ 1/2 1/2 0
Change of Basis : Matrix Representation
Please see the attached file for full problem description. Let E= {1, x, x^2, x^3} be the standard ordered basis for the space P_3. G= {1+x, 1-x, 1-x^2, 1-x^3} is also a basis for P_3. Write the matrix representation [p(x)]_G for the polynomial (vector) p(x)=3x^3-2x+4 from P_3 with respect to the basis G. Show work.
Proof: Hermitian Adjoint and Orthonormal Bases
Please see the attached file for full problem description. 1.Write a proof for the following statement: For every n x n complex matrices A and B, (AB)*= B*A*. Show work. Help:  : is "alpha" with a line above it. *: is the Hermitian adjoint
Determinants and Adjugate : Proof
Please see the attached file for the fully formatted problems. --- 1. Write a proof for the following statement: If A is any n x n non-singular matrix, then det(adj(A))=(det(A))^(n-1). Show work. Help: det: is the determinant adj: is the adjugate (or classical adjoint)
Matrix Proof: Determinants
Please see the attached file for the full problem description: 1. Show that if   0, then A^-1=1/ [ d -b ] [ -c a ] . Help: : is the determinant A [ d -b] [ -c a ] : is a 2 x 2 matrices
System of Equations: Solve using Inverse of Coefficient Matrix
Solve the following system of equations by computing the inverse of the coefficient matrix. -x+2y =4 2x-y+2z = -2 2y-z = 4
Systems of Equations : Solve using Augmented Matrix
Solve the following system of equations by performing elementary row operations on the augmented matrix. x1-2x2 +2x4 = 6 2x1-4x2+x3-x4 =-2 3x1+6x2-x3-x4=-4 x1-2x2+x3-3x4=-8
Matrix of T(x,y) = (4x - 2y, 2x + y) relative to the basis
Linear Algebra Matrix of the Linear Map Basis of the Linear Space Let T be a linear map on R^2 defined by T(x,y) = (4x - 2y, 2x + y). Calcu
3 men paint a fence. How long will it take each of them to paint the fence by himself? Use Gaussian elimination.
Solve using the Gaussian Elimination and show all work. Mike, Joe and Bill are Painting a fence. The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours, or if Mike and Joe work together for 2 hours, and Bill works alone for 5 hours, or if Mike works alone for 6 hours, Joe works
Matrix Proof: Row Equivalence
2. Write a matrix algebra proof for the following statement: Let A and B be nxm matrices. If A is row equivalent to B, then B is row equivalent to A. Show work.
Determinant of the Van der Monde Matrix
The Vandermonde matrix is defined the following way. Suppose x1,x2,...xn are n numbers. Form the nxn matrix: A=(1 x1 x1^2 ... x1^(n-1) ) (1 x2 x2^2 ... x2^(n-1) ) (... ) (1 xn xn^2 ... xn^(n-1) ) Find determinant A.
Fundamental subspace theorem
Consider the matrix a=(1 1 2 1 2 -1 3 2 1 5 5 2) Find N(A), R(A), N(A^T),R(A^T). Show that the fundamental subspace theorem holds: N(A^T)=R(A)^(upside down T), N(A)=R(A^T)^(upsidedown T). Hint: Notice that the fourth row is the sum of the first three rows.
Show that a given matrix is symmetric and idempotent
Let X be a txk matrix whose columns are linearly independent. Let M=I-X(X'X)^(-1)X'. Show that M is symmetric and idempotent.
Investigate the Automorphism Group of Z_p + Z_{p^2}
Investigate the Automorphism Group of Z_p + Z_{p^2}. Please see the attached file.
Solution for an IVP differential equation problem
Using the method of undetermined coefficients, find the solution of the system: X'=AX + B that satisfies the initial condition: X(0)=( 0 1 -1). A and B are matrices defined in the attached Notepad file. Note: When solving the homogeneous soln, exhibit a fundamental matrix psi(t) and al
A proof that for a self adjoint linear operator T
Prove that for any self-adjoint bounded linear operator T on a Hilbert space H that (Tf,f) is real-valued for all f in H.
Working with matrices : Determinants and transposes.
If A is a 3x3 matrix such that the determinant A is 2 and A1 is the transpose of A, find the determinant of A1.
Inverses of 2 x 2 matrices made easy!
Find the inverse of the following 2x2 matrix: | 1 2 | | 3 4 |
Find the matrix products.
Find the matrix products.
Addition and subtraction of matrices
Please see the attached file for the fully formatted problems. Solve the following matrix problems.
Subtraction of matrices
Please see the attached file for the fully formatted problem.
Solve the system of equations by the Gaussian elimination method
17. Solve the system of equations by the Gaussian elimination method. x- 3y + z= 8 2x- 5y -3 z= 2 x + 4y + z= 1 18. Find the inverse of the given matrix. 1 2 -2 -3 19. Evaluate the determinant by expanding by cofactors. -2 3 2 1 2 -3 -4 -2 1 20. Solve the system of
Discrete Math: Matrix Operations (proofs)
Prove or disprove that, for matrices A,B,C for which the following operations are defined: a. A*(B+C) = A*B + A*C b. A+(B*C) = (A+B)(A+C)
Inverse Matrix
I have tried numerous times, I just don't get it. Problem: Find the Inverse [4 1] [3 1]
Roots of non singular matrix. Proof
Show that if lamda is a characteristic root of a non-singular matrix A, then lamda^-1 is a characteristic root of A^-1.
Matrices
Matrices problem attached
Matrices
When Finding the product how many pairs of numbers must be multiplied together?