Question

Determine a matriz transposta de C= (Cij)3x2 com Cij = i^2 - 2j^2

Answer 1

C = (Cij)3x2  => 3 linhas e duas colunas

$\left[\begin{array}{ccc}c11&c12\\c21&c22\\c31&c32\end{array}\right]$

Cij = i² - 2j²

C11 = 1² - 2(1)²
C11 = 1 - 2(1)
C11 = 1 - 2
C11 = - 1

C12 = 1² - 2(2)²
C12 = 1 - 2(4)
C12 = 1 - 8
C12 = - 7

C21 = 2² - 2(1)²
C21 = 4 - 2(1)
C21 = 4 - 2
C21 = 2

C22 = 2² - 2(2)²
C22 = 4 - 2(4)
C22 = 4 - 8
C22 = - 4

C31 = 3² - 2(1)²
C31 = 9 - 2(1)
C31 = 9 - 2
C31 = 7

C32 = 3² - 2(2)²
C32 = 9 - 2(4)
C32 = 9 - 8
C32 = 1

$C= \left[\begin{array}{ccc}-1&-7\\2&-4\\7&1\end{array}\right]$

$c^{t} = \left[\begin{array}{ccc}c11&c21&c31\\c21&c22&c23\\\end{array}\right]$

$C^{t} = \left[\begin{array}{ccc}-1&2&7\\-7&-4&1\\\end{array}\right]$