Question

Gente me ajudem nesse

Answer 1

A) Construir a matriz B.
$B = \left[\begin{array}{ccc}a11&a12&a13\\a21&22&a23\\a31&a32&a33\end{array}\right]$
$B = \left[\begin{array}{ccc}1^{3} &0&0\\2^{3}&2^{3}&0\\3^{3}&3^{3}&3^{3}\end{array}\right]$
$B = \left[\begin{array}{ccc}1&0&0\\8&8&0\\27&27&27\end{array}\right]$

B) Achar os valores de a, b, c e d
$\left[\begin{array}{ccc}a + b&b+c\\2b&2a-3d\end{array}\right] = \left[\begin{array}{ccc}9&-1\\6&18\end{array}\right] \\ \\ a+b = 9 \\ b+c = -1 \\ 2b = 6 \\ 2b-3d = 18 \\ \\ b = 6/2 \\ b = 3 \\ \\ a + 3 = 9 \\ a = 9-3 \\ a = 6 \\ \\ 3 + c = -1 \\ c = 3-1 \\ c = 2 \\ \\ 2*3 - 3d = 18 \\ -3d = 12 \\ d = -12/3 \\ d = -4$

C) A = aij    //    aij = 2i - 3j   //   X + 2A = B
$\left[\begin{array}{ccc}a11&a12\\a21&a22\end{array}\right]$
$A = \left[\begin{array}{ccc}2*1 - 3*1&2*1 - 3*2\\2*2 - 3*1&2*2 - 3*2\end{array}\right] \\ A = \left[\begin{array}{ccc}2 - 3&2 - 6\\4 - 3&4 - 6\end{array}\right] \\ A =\left[\begin{array}{ccc}-1&-4\\1&-2\end{array}\right] \\ \\ 2A = 2*\left[\begin{array}{ccc}-1&-4\\1&-2\end{array}\right] \\ 2A = \left[\begin{array}{ccc}-2&-8\\2&-4\end{array}\right] \\ X + \left[\begin{array}{ccc}-2&-8\\2&-4\end{array}\right] = \left[\begin{array}{ccc}1&0\\-1&1\end{array}\right]$
$X = \left[\begin{array}{ccc}1&0\\-1&1\end{array}\right] - \left[\begin{array}{ccc}-2&-8\\2&-4\end{array}\right] \\ X = \left[\begin{array}{ccc}1-(-2)&0 -(-8)\\-1 - 2&1 -(-4)\end{array}\right] \\ X = \left[\begin{array}{ccc}1+2&8\\-3&1+4\end{array}\right] \\ X = \left[\begin{array}{ccc}3&8\\-3&5\end{array}\right]$