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Matrices

Diagonal Matrix

Diagoalize te given matrix: A= 3 1 1 1 0 2 1 2 0 an find an orthogonal matrix P such that P'-1(Pinverse)AP is diagonal.

Symmetric matrix

What is the symmetric matrix of the quadratic form 2x^2 - 8xy + 4y^2?

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

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

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