En cada literal determina xey de modo que se verifique la igualdad de matrices.
Respuestas a la pregunta
Respuesta:
Cada literal x e y, que verifica la igualdad de matrices es:
a) x = 2 ; y = 0
b) x = 5 ; y = -6
c) x = 2 ; y = 1
Explicación paso a paso:
Una matriz es
\begin{gathered}\left[\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right] = \left[\begin{array}{cc}a'_{11}&a'_{12}\\a'_{21}&a'_{22}\end{array}\right]\end{gathered}
[
a
11
a
21
a
12
a
22
]=[
a
11
′
a
21
′
a
12
′
a
22
′
]
Siendo;
a₁₁ = a'₁₁
a₁₂ = a'₁₂
a₂₁ = a'₂₁
a₂₂ = a'₂₂
\begin{gathered}a) \left[\begin{array}{cc}2&3\\1&0\end{array}\right]= \left[\begin{array}{cc}x&3\\1&y\end{array}\right]\end{gathered}
a)[
2
1
3
0
]=[
x
1
3
y
]
Igualar cada literal;
2 = x
3 = 3
1 = 1
0 = y
\begin{gathered}b)\left[\begin{array}{cc}-1&5\\-2&8\end{array}\right] = \left[\begin{array}{cc}x+y&x\\-2&8\end{array}\right]\end{gathered}
b)[
−1
−2
5
8
]=[
x+y
−2
x
8
]
Igualar cada literal;
-1= x+y
5 = x
-2 = -2
8=8
Sustituir x = 5;
-1 = 5+y
y = -6
\begin{gathered}c)\left[\begin{array}{cc}4+y&3\\2-y&1\end{array}\right] =\left[\begin{array}{cc}2x+5&3\\y&1\end{array}\right]\end{gathered}
c)[
4+y
2−y
3
1
]=[
2x+5
y
3
1
]
Igualar cada literal;
4x+y = 2x+5
3 = 3
2-y = y
1 = 1
2y = 2
y = 1
sustituir;
4x+1 = 2x+5
2x = 4
x = 2