Question

1- dada as matrizes A e B calcule o que se pede :
A- 3 4 e            B-          2 1 0
     2 1                             -3 1 2
                                        2 4 5

a- det (A)=
b- det (A)=
c- det (B)=
d- det (B^t)=

Answer 1

$<var>a) e b) A:\left[\begin{array}{ccc}3&4\\2&1\end{array}\right]=(3.1)-(4.2)=3-8=>det(A)=-5\\\\c) B: \left[\begin{array}{ccc}2&1&0\\-3&1&2\\2&4&5\end{array}\right]\\=[(2.1.5)+(-3.4.0)+(1.2.2)]-[(0.1.2)+(2.4.2)+(-3.1.5)]\\=[10+0+4]-[0+16-15]=14-1=>det(B)=13</var>$

$<var>B^t: \left[\begin{array}{ccc}2&-3&2\\1&1&4\\0&2&5\end{array}\right]\\\\=[(2.1.5)+(-3.4.0)+(1.2.2)]-[(2.1.0)+(4.2.2)+(-3.1.5)]\\=[10+0+4]-[0+16-15]=14-1=>det(B^t)=13</var>$