## Linear Algebra and Its Applications, exercise 1.4.6

Exercise 1.4.6. Find the 3×2 matrix A for which $a_{ij} = i + j$. Find the 3×2 matrix B for which $b_{ij} = (-1)^{i+j}$.

$A = \begin{bmatrix} 1+1&1+2 \\ 2+1&2+2 \\ 3+1&3+2 \end{bmatrix} = \begin{bmatrix} 2&3 \\ 3&4 \\ 4&5 \end{bmatrix}$
$B = \begin{bmatrix} (-1)^{1+1}&(-1)^{1+2} \\ (-1)^{2+1}&(-1)^{2+2} \\ (-1)^{3+1}&(-1)^{3+2}\end{bmatrix} = \begin{bmatrix} (-1)^2&(-1)^3 \\ (-1)^3&(-1)^4 \\ (-1)^4&(-1)^5 \end{bmatrix} = \begin{bmatrix} 1&-1 \\ -1&1 \\ 1&-1 \end{bmatrix}$