Question #291381

Given that k =[2 1]




[3 4]




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






1
Expert's answer
2022-01-31T12:55:42-0500
K2=[2134][2134]K^2=\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}

=[2(2)+1(3)2(1)+1(4)3(2)+4(3)3(1)+4(4)]=[761819]=\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}

K2+K+I=[761819]+[2134]+[1001]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}

=[7+2+16+1+018+3+019+4+1]=[1072124]=\begin{bmatrix} 7+2+1 & 6+1+0 \\ 18+3+0 & 19+4+1 \end{bmatrix}=\begin{bmatrix} 10 & 7 \\ 21 & 24 \end{bmatrix}

K2+2K+I=[1072124]K^2+2K+I=\begin{bmatrix} 10 & 7 \\ 21 & 24 \end{bmatrix}


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