Question

Ajutor la punctul c)

Answer 1

[tex]X=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] A(2) * X = A(5) \left[\begin{array}{ccc}1&2\\2&3\end{array}\right] * \left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = \left[\begin{array}{ccc}1&2\\5&6\end{array}\right] \left[\begin{array}{ccc}a+2c&b+2d\\2a+3c&2b+3d\end{array}\right]=\left[\begin{array}{ccc}1&2\\5&6\end{array}\right] [/tex]

Faci sistem de ecuatii
a + 2c = 1
b + 2d = 2
2a + 3c = 5
2b + 3d = 6

Luam ecuatiile

a + 2c = 1
2a + 3c = 5

Inmultim pe prima cu (-2) si obtinem sistemul
-2a - 4c = -22a + 3c = 5
Adunam cele 2 ecuatii si obtinem
-c = 3  rezulta c = -3
Inlocuim pe c in ecuatia 2a + 3c = 5
2a + 3c = 52a + 3 * (-3) = 52a - 9 = 52a = 5 + 92a = 14a = 14/2a = 7

Acum luam celelalte 2 ecuatii din cele 4 initialeb + 2d = 2
2b + 3d = 6
Inmultim pe prima cu (-2)-2b -4d = -42b + 3d = 6
Le adunam-d = 2 rezulta d = -2
Inlocuim pe d in ecuatia 2b + 3d = 62b + 3d = 62b + 3 * (-2) = 62b - 6 = 62b = 12b = 6
Deci matricea X va arata asa:
$X = \left[\begin{array}{ccc}7&6\\-3&-2\end{array}\right]$