Exercise 4.12

Enter matrix $ A$ and the vector $ v$ = [1 2 3 4].

$\displaystyle A = \begin{bmatrix}1 & 2 & -1 & 3 \\ 7 & 2 & 0 & 1 \\ 3 &-2 & -1 &-1 \\ 0 & 1 & 4 & 8 \end{bmatrix}$    

a)
Calculate $ vA$ and $ Av^T$ . What happens with the rows and columns of the matrix when performing these multiplications?
b)
Make a diagonal matrix $ D$ which has the elements of $ v$ on the diagonal. Calculate $ DA$ and $ AD$ . What happens with the rows and columns of the matrix when performing these multiplications?



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Esteur 2010-03-22