# Thread: How do I solve this? Linear Algebra.

1. ## How do I solve this? Linear Algebra.

Find the upper triangular matriz A such that A^3 = (8, -57 and second row 0, 27).

Can anyone help?

2. Hi,

Let $A=\left(\begin{smallmatrix}x & y\\ 0 & z\end{smallmatrix}\right)$. If you compute $A^3$ you'll get
$A^3=\begin{pmatrix}{x}^{3} & y\left({z}^{2}+xz+x^2 \right) \cr 0 & {z}^{3}\end{pmatrix}$

so you have to solve
$\begin{pmatrix}{x}^{3} & y\left({z}^{2}+xz+x^2 \right) \cr 0 & {z}^{3}\end{pmatrix}=\begin{pmatrix}8&-57\\0 & 27 \end{pmatrix}$
for $x$, $y$ and $z$.