Question

Which of the following matrices are symmetric? Which ones are orthogonal? (a) A=[1 1; 1 1] (b) B=[1/ ... Answer 1-3 and show work please!Calculus 2 Lab 5 Name On this page we investigate upper bounds for the error when using the midpoint, trapezoid, and Simpson's rule. In order to find the K value mentioned in the formulas,

Answer 1

Matrix (a) A=[1 1; 1 1] is symmetric because A is equal to its transpose, AT, but it is not orthogonal as A * AT does not yield the identity matrix.

Step-by-step explanation:

To determine which matrices are symmetric and which are orthogonal, we review the definitions of these types of matrices. A symmetric matrix is equal to its transpose (flipping across the main diagonal), and an orthogonal matrix has its transpose equal to its inverse, such that the product of the matrix and its transpose results in the identity matrix.

For matrix (a) A=[1 1; 1 1], it is symmetric because if you take the transpose of the matrix, you get the same matrix: AT = [1 1; 1 1], confirming it's symmetric. However, it is not orthogonal because the product of A and AT does not yield the identity matrix.

Without the complete matrices for the other parts of the question, the symmetry and orthogonality cannot be determined. The example matrix (a) helps to illustrate the process: check transpose for symmetry and check the identity result for orthogonality.