Number of matrices

[man111]

Number of [tex]3\times 3[/tex] diagonal matrices [tex]P[/tex] with real entries satisfying [tex]\displaystyle P^3-7P^2+14P-8I = O[/tex], is

[grav]

If [tex]P=\begin{pmatrix}
a&0&0\\
0&b&0\\
0&0&c
\end{pmatrix}[/tex]

then [tex]a[/tex], [tex]b,[/tex] and [tex]c[/tex] are solutions of [tex]x^3-7x^2+14x-8=0[/tex], which has solutions [tex]1, 2,[/tex] and [tex]4[/tex]. So there are 8 such matrices.

[pipi langstrump]

Не са ли 27?

[grav]

Не са ли 27?

Уф, да!