Question 4.1.2: Consider the 2 × 2 matrix K defined by K = [ k1 + k2 - k2 -k......
Consider the 2 × 2 matrix K defined by
K=\left[\begin{array}{cc} k_1+k_2 & -k_2 \\ -k_2 & k_2 \end{array}\right] (4.9)
and calculate the product Kx.
Again, the product is formed by considering the first element to be the inner product of the row vector \left[\begin{array}{ll}k_1+k_2 & -k_2\end{array}\right] and the column vector x. The second element of the product vector K x is formed from the inner product of the row vector \left[\begin{array}{ll}-k_2 & k_2\end{array}\right] and the vector x. This yields
K x =\left[\begin{array}{cc} k_1+k_2 & -k_2 \\ -k_2 & k_2 \end{array}\right]\left[\begin{array}{l} x_1 \\ x_2 \end{array}\right]=\left[\begin{array}{c} \left(k_1+k_2\right) x_1-k_2 x_2 \\ -k_2 x_1+k_2 x_2 \end{array}\right] (4.10)