Question

sejam as matrizes
A= ( 1 2 3
0 1 2
2 1 0)

B= (-1/2 2 6
0 3 1
-1 4 3) e C= A+2B. calcule a determinante da matriz C​

Answer 1

$A=\begin{bmatrix}1&2&3\\0&1&2\\2&1&0\end{bmatrix}$

$B=\begin{bmatrix}-\frac{1}{2}&2&6\\0&3&1\\-1&4&3\end{bmatrix}$

$C=\begin{bmatrix}1&2&3\\0&1&2\\2&1&0\end{bmatrix}+2.\begin{bmatrix}-\frac{1}{2}&2&6\\0&3&1\\-1&4&3\end{bmatrix}$

$C=\begin{bmatrix}(1-1)&(2+4)&(3+12)\\(0+0)&(1+6)&(2+2)\\(2-2)&(1+8)&(0+6)\end{bmatrix}$

$C=\begin{bmatrix}0&6&15\\0&7&4\\0&9&6\end{bmatrix}$

$detC=0\begin{bmatrix}7&4\\9&6\end{bmatrix}-6\begin{bmatrix}0&4\\0&6\end{bmatrix} +15\begin{bmatrix}0&7\\0&9\end{bmatrix}$

$\boxed{\boxed{detC=0}}$

Answer 2

Resposta:

A=

( 1 2 3  

0 1 2  

2 1 0)

B=

(-1/2 2 6

   0   3  1

  -1  4   3)

2B =

(-1   4  12

0   6    2

-2   8    6

A+2B=

(1-1 = 0      2+4=6      3+12=15)

(0+0=0     1+6=7       2+2=4 )

2-2=0         1+8=9        0+6  = 6)

a primeira coluna =0   ==> determinante = 0