Question 4.1.3: Consider the matrix A defined by A = [ a b c d ] where a, b,......

Solution For A to be symmetric, A=A^T or

A=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]=\left[\begin{array}{ll} a & c \\ b & d \end{array}\right]=A^T 

Comparing the elements of A and A^T yields that c=b must hold if the matrix A is to be symmetric. Note that the elements in the c and b position of the matrix K given in equation (4.9) are equal so that K=K^T.

K=\left[\begin{array}{cc} k_1+k_2 & -k_2 \\ -k_2 & k_2 \end{array}\right]           (4.9)