Question

calculati determinantul formand elemente 0 pe prima linie ​

Answer 1

Răspuns:

$\left[\begin{array}{cccc}2&-1&1&1\\1&-3&2&0\\5&2&-1&5\\1&-1&4&-6\end{array}\right] =$

Explicație pas cu pas:

Adunam a doua coloana la a treia coloana :

$=\left[\begin{array}{cccc}2&-1&1-1&1\\1&-3&2-3&0\\5&2&-1+2&5\\1&-1&4-1&-6\end{array}\right] =$

$=\left[\begin{array}{cccc}2&-1&0&1\\1&-3&-1&0\\5&2&1&5\\1&-1&3&-6\end{array}\right] =$

Adunam a doua coloana la a patra coloana :

$=\left[\begin{array}{cccc}2&-1&0&1-1\\1&-3&-1&0-3\\5&2&1&5+2\\1&-1&3&-6-1\end{array}\right] =$

$=\left[\begin{array}{cccc}2&-1&0&0\\1&-3&-1&3\\5&2&1&7\\1&-1&3&-7\end{array}\right] =$

Adunam dublul celei de a doua  coloane la prima coloana :

$=\left[\begin{array}{cccc}2+2*(-1)&-1&0&0\\1+2*(-3)&-3&-1&3\\5+2*2&2&1&7\\1+2*(-1)&-1&3&-7\\\end{array}\right] =$

$=\left[\begin{array}{cccc}2-2&-1&0&0\\1-6&-3&-1&3\\5+4&2&1&7\\1-2&-1&3&-7\\\end{array}\right] =$

$=\left[\begin{array}{cccc}0&-1&0&0\\-5&-3&-1&3\\9&2&1&7\\-1&-1&3&-7\\\end{array}\right] =$

$= (-1)*(-1)*(-1)*7 - (-5)*(-1)*3*7 =\\=-7 -105 = -112$