Resposta:
a ) A = [tex]\left[\begin{array}{ccc}0&-1\\1&0\\\end{array}\right][/tex]
b) B = [tex]\left[\begin{array}{ccc} 4&9&16\\9&16&25\\\end{array}\right][/tex]
c) C = | 3 - 3 3 - 7 |
d) D = [tex]\left[\begin{array}{ccc}1&3\\3&2\\4&5\end{array}\right][/tex]
Explicação passo-a-passo:
Escreva as matrizes:
a) A(2x2) onde aij = i - j
[tex]\left[\begin{array}{ccc}a11&a12\\a21&a22\\\end{array}\right][/tex]
A = [tex]\left[\begin{array}{ccc}1-1&1-2\\2-1&2-2\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}0&-1\\1&0\\\end{array}\right][/tex]
b) B (2x3) onde bij = ( i + j )²
[tex]\left[\begin{array}{ccc}a11&a12&a13\\a21&a22&a23\\\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}(1+1)^{2} &(1+2)^2&(1+3)^2\\(2+1)^2&(2+2)^2&(2+3)^2\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc} 4&9&16\\9&16&25\\\end{array}\right][/tex]
c) C (1x4) cij → i² - 2j se j par
→ 3 se j ímpar
C = | a11 a12 a13 a14 |
C = | 3 1²-2*2 3 1² - 2*4 |
C = | 3 - 3 3 - 7 |
d) D (3x2) dij → i se i = j
→ i + j se i ≠ j
D = [tex]\left[\begin{array}{ccc}a11&a12\\a21&a22\\a31&a32\end{array}\right][/tex]
D = [tex]\left[\begin{array}{ccc}1&3\\3&2\\4&5\end{array}\right][/tex]
Bom estudo.
