Diagonal and Orthogonal Matrix

Linear Algebra Matrices (IX) Orthoganal Matrix Show that the matrix A = [-8/9, 4/9 , 1/9; 1/9 , 4/9 , -8/9; 4/9

Please show the complete steps. 1. Let T: P2 -> P1 be the linear transformation defined by T(p(x)) = p'(x) + p(x). Show that T is linear. 2. Find the matrix for the transformation T given in problem 1 with respect to the standard basis {1, x, x^2}. Then, find all eigenvalues and corresponding eigenvectors for T. 3. True

Let A be a 3 x 3 real orthogonal matrix with det A = 1. Prove that λ= 1 is an eigenvalue of A.

R stands for the field of real numbers. C stands for the field of complex numbers. 1. Let T be a linear transformation from the set P2(R) of all polynomials of degree at most 2 into itself. T: P2(R) --> P2(R), given by T(f) = f' - f'', fEP2(R), where f' is the first and f'' is the second derivative of f. (a) Find the null

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

Please prove the properties of condition numbers attached to this message. Refer to definitions/theorems you used. Also, if you want, have a look at the second file attached, since I believe that you can refer to the previous properties to do 6 to 10. 7. For any orthogonal matrix Q, i2(QA) = k2(AQ) = k2(A) 8. If D= diag(d1,

Identify and sketch the graph of the conic described by the quadratic equation x^2 + 4xy + y^2 - 12 = 0. Do this by writing this equation in matrix form; then change the equation to a sum of squares of the form x'^T Dx' where D is a diagonal matrix.

Dtermine whether or not the following matrix A= 5 0 2 0 5 0 2 0 5 is diagonalizable. If it is, then determine P'-1(P inverse)AP.

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)