Question

|2 4 -1 2|

|-1 2 3 1|

|2 5 1 4|

|1 2 -2 3|

визначник..........хто знає вищу математику????((((HELLP!!!!

Answer 1

$left|begin{array}{cccc}2&4&-1&2\-1&2&3&1\2&5&1&4\1&2&-2&3end{array}right|=$

 

$=(-1)^{1+1}cdot2left|begin{array}{ccc}2&3&1\5&1&4\2&-2&3end{array}right|+(-1)^{1+2}cdot4left|begin{array}{ccc}-1&3&1\2&1&4\1&-2&3end{array}right|+ \ (-1)^{1+3}cdot(-1)left|begin{array}{ccc}-1&2&1\2&5&4\1&2&3end{array}right|+(-1)^{1+4}cdot2left|begin{array}{ccc}-1&2&3\2&5&1\1&2&-2end{array}right|=$

 

$=2((-1)^{1+1}cdot2left|begin{array}{cc}1&4\-2&3end{array}right|+(-1)^{1+2}cdot3left|begin{array}{cc}5&4\2&3end{array}right|+(-1)^{1+3}left|begin{array}{cc}5&1\2&-2end{array}right|)-$

$-4((-1)^{1+1}cdot(-1)left|begin{array}{cc}1&4\-2&3end{array}right|+(-1)^{1+2}cdot3left|begin{array}{cc}2&4\1&3end{array}right|+(-1)^{1+3}left|begin{array}{cc}2&1\1&-2end{array}right|)-$

$-((-1)^{1+1}cdot(-1)left|begin{array}{cc}5&4\2&3end{array}right|+(-1)^{1+2}cdot2left|begin{array}{cc}2&4\1&3end{array}right|+(-1)^{1+3}left|begin{array}{cc}2&5\1&2end{array}right|)-$

$-2((-1)^{1+1}cdot(-1)left|begin{array}{cc}5&1\2&-2end{array}right|+(-1)^{1+2}cdot2left|begin{array}{cc}2&1\1&-2end{array}right|+(-1)^{1+3}cdot3left|begin{array}{cc}2&5\1&2end{array}right|)=$

=2(2(1*3-4*(-2))-3(5*3-4*2)+(5*(-2)-1*2)) -4(-(1*3-4*(-2))-3(2*3-4*1)+(2*(-2)-1*1) -(-(5*3-4*2)-2(2*3-4*1)+(2*2-5*1)) -2(-(5*(-2)-1*2)-2(2*(-2)-1*1)+3(2*2-5*1))=40