Sabendo que A={4 2 0 1} e B={1 0 0 1} obtenha as matrizes M e N tais que {2m+N=A-B}{m+3N=2A+B}
Respostas
Resposta:
Explicação passo-a-passo:
Sabendo que:
A=
{4 2
0 1}
B
=
{1 0}
{0 1}
obtenha as matrizes M e N tais que:
2m+N=A-B
m+3N=2A+B
A - B
A=
{4 2
0 1}
B
(-)
=
{1 0}
{0 1}
=
3 2
0 0
2A +B
2. A
A=
{4 2}
{0 1}
=
8 4
0 2
(+) (B)
{1 0}
{0 1}
=
9 4
0 3
2M + N =
3 2
0 0
M + 3N =
9 4
0 3
2.M
2a 2b
2c 2d
(+)
r s
t u
=
3 2
0 0
2a + r = 3 2b+s = 2
2c + t = 0 2d + u = 0
M (+) 3N =
9 4
0 3
a b
c d
(+)
3r 3s
3t 3u
=
9 4
0 3
a + 3r = 9 b + 3s = 4
c + 3t = 0 d + 3u = 3
2a + r = 3
a + 3r = 9 (-2)
2a + r = 3
-2a - 6r = - 18
-5r = -15 (-1)
5r = 15
r = 15/5
r = 3
2a + r = 3
2a + 3 = 3
2a = 0
a = 0
c + 3t = 0
2c + t = 0
c = - 3t
2c+t = 0
2.(-3t)+t = 0
-6t+t = 0
-5t = 0
t = 0
c = - 3t
c = -3.0
c = 0
b+3s = 4 (-2)
2b+s = 2
-2b -6s = -8
2b +s = 2(+)
-5s = -6 (-1)
5s = 6
s = 6/5
2b + s = 2
2b + 6/5 = 2
(5.2b + 6)/5 = 5.2/5
10b+6= 10
10b = 10-6
10b = 4 (:2)
5b = 2
b = 2/5
d+3u = 3
2d + u = 0
u = -2d
d+3u = 3
d+3.(-2d)= 3
d-6d = 3
-5d = 3 (-1)
5d = -3
d = -3/5
u = -2d
u = -2.(-3/5)
u = 6/5
M =
a b
c d
=
[0 2/5]
[0 -3/5]
N
=
r s
t u
=
[3 6/5]
[0 6/5]
R.:
M =
[0 2/5]
[0 -3/5]
N
=
[3 6/5]
[0 6/5]