Question

se considera matricea A=(1,1,1,0) a)calculati A2-A,​

Answer 1

A = $\left[\begin{array}{ccc}1&1\\1&0\end{array}\right]$

A² = $\left[\begin{array}{ccc}1&1\\1&0\end{array}\right]$ · $\left[\begin{array}{ccc}1&1\\1&0\end{array}\right]$ =

( Pentru a înțelege mai ușor )

a₁₁ = 1 · 1 + 1 · 1 = 2

a₁₂ = 1 · 1 + 1 · 0 = 1

a₂₁ = 1 · 1 + 0 · 1  = 1

a₂₂ = 1 · 1 + 0 · 0 = 1

Deci o să avem:

A² = $\left[\begin{array}{ccc}2&1\\1&1\end{array}\right]$

A² - A = $\left[\begin{array}{ccc}2&1\\1&1\end{array}\right]$ - $\left[\begin{array}{ccc}1&1\\1&0\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$