Answer to Question #291381 in Linear Algebra for Rossy

Question

Given that k =[2 1]

[3 4]

Find the matrix k2+k+i,where i is the (2× 2) identify matrix

Answer 1

$$K^2=\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}$$

$$=\begin{bmatrix} 2(2)+1(3) & 2(1)+1(4) \\ 3(2)+4(3) & 3(1)+4(4) \end{bmatrix}=\begin{bmatrix} 7 & 6 \\ 18 & 19 \end{bmatrix}$$

$$K^2+K+I=\begin{bmatrix} 7 & 6 \\ 18 & 19 \end{bmatrix}+\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}+\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$=\begin{bmatrix} 7+2+1 & 6+1+0 \\ 18+3+0 & 19+4+1 \end{bmatrix}=\begin{bmatrix} 10 & 7 \\ 21 & 24 \end{bmatrix}$$

$$K^2+2K+I=\begin{bmatrix} 10 & 7 \\ 21 & 24 \end{bmatrix}$$