Question

calcule o valor do determinante da matriz
A) 3 2 5
-4 1 3
2 3 4

B ) 0 3 0
-2 3 1
4 -2 5

C) 2 2 0
1 1 1
4 3 0

D) 4 -1 0
5 7 6
-1 3 8

E) -4 6 -9
-3 4 6
2 1 3



me ajuda gente

Answer 1

a)

$\left[\begin{array}{ccc}3&2&5\\-4&1&3\\2&3&4\end{array}\right] \left\begin{array}{cc}3&2\\-4&1\\2&3\end{array}\right \\ \\ \\ 3*1*4+2*3*2+5*-4*3-2*1*5-3*3*3-4*-4*2=-41 \\ \\ Det . = -41$

===

b)

$\left[\begin{array}{ccc}0&3&0\\-2&3&1\\4&-2&5\end{array}\right] \left[\begin{array}{cc}0&3\\-2&3\\4&-2\end{array}\right]$

0*3*5+3*1*4+0*-2*-2-4*3*0--2*1*0-5*-2*3=42

Det. = 42

===

c)

$\left[\begin{array}{ccc}2&2&0\\1&1&1\\4&3&0\end{array}\right] \left\begin{array}{cc}2&2\\1&1\\4&3\end{array}\right \\ \\ \\2*1*0+2*1*4+0*1*3-4*1*0-3*1*2-0*1*2=2 \\ \\ Det. = 2$

===

d)


$\left[\begin{array}{ccc}4&-1&0\\5&7&6\\-1&3&8\end{array}\right] \left\begin{array}{cc}4&-1\\5&7\\-1&3\end{array}\right$

4*7*8+-1*6*-1+0*5*3--1*7*0-3*6*4-8*5*-1=198

Det. = 198

====

e)

$\left[\begin{array}{ccc}-4&6&-9\\-3&4&6\\2&1&3\end{array}\right] \left\begin{array}{cc}-4&6\\-3&4\\2&1\end{array}\right$

-4*4*3+6*6*2+-9*-3*1-2*4*-9-1*6*-4-3*-3*6=201

Det. = 201