Question

seja A = (aij)2x2 tal que aij =  4i – 3j. calcule det A

Answer 1

$A=(a_{ij})_{2\times2}$, tal que, $a_{ij}=4i-3j$.

$\left(\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right)$

$a_{11}$

$i=1$, $j=1$

$a_{11}=4\cdot1-3\cdot1=4-3=1$


$a_{12}$

$i=1$, $j=2$

$a_{12}=4\cdot1-3\cdot2=4-6=-2$

$a_{21}$

$i=2$, $j=1$

$a_{21}=4\cdot2-3\cdot1=8-3=5$


$a_{22}$

$i=2$, $j=2$

$a_{22}=4\cdot2-3\cdot2=8-6=2$

$\left(\begin{array}{cc}1&-2\\5&2\end{array}\right)$

Diagonal principal:

$1\cdot2=2$

Diagonal secundária:

$(-2)\cdot5=-10$


$\text{det}_{A}=2-(-10)=2+10=12$.