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Matrices

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: 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.

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

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

Inverse Matrix

I have tried numerous times, I just don't get it. Problem: Find the Inverse [4 1] [3 1]

Matrices

When Finding the product how many pairs of numbers must be multiplied together?

Gaussian Elimination

Solve the system of equations by the Gaussian elimination method. Which of the following is NOT a matrix leading to the solution?

Solve the system of equations

QUESTION: Solve the system of equations by the Gaussian elimination method. 2x + y –3z =1 3x - y + 4z =6 x + 2y - z =9 My response: Please explain if I am wrong. I have several more to do. 2 1 -3 1 3 -1 4 6 1 2 -1 9

Process of Gaussian Elimination

X+Y+2z=6 3X+2Y+Z=9 X-Y=4 Use the system in above. Without interchanging any of the rows in the augmented matrix, what is the first value, which will be replaced with zero when using the Gaussian Elimination method?

Matrices

DAY 1. Multiply the three matrices together in order (A*B*C) to get a fourth matrix 'D'. What is the fourth matrix? DAY 2. Multiply the fourth matrix by the scalar 6 to get a fifth matrix E. DAY 3. Add the fifth matrix to a matrix whose elements are all "2"'s to get a sixth matrix F. What is the sixth matrix? DAY 4.

Matrix Theory

Show that each matrix type is normal. 1. Hermitian 2. skew-Hermitian 3. unitary 4. symmetric 5. skew-symmetric 6. orthogonal

Matrix Theory

Prove that for in H, Thus, N is a homomorphism from onto the positive real numbers. See attached file for full problem description.

Matrix Theory/ Isometries

Fix in Consider the real linear map given by (a) With respect to the basis B = {1, i, j, k}, find the associated matrix for . (b) Find the associated matrix A (sub alpha bar) for M (sub alpha bar). Compare with (a). (c) Compute det(A sub alpha) and det (A sub alpha bar). Interpret. See attached file for ful