In the 2 × 2 linear systems that follow, the system (B) is obtained from (A) by performing the elementary operation E 2 + c E 1 . Prove that any solution, x 1 = s 1 , x 2 = s 2 , for (A) is a solution for (B). Similarly, prove that any solution, x 1 = t 1 , x 2 = t 2 , for (B) is a solution for (A). (A) a 11 x 1 + a 12 x 2 = b 1 a 21 x 1 + a 22 x 2 = b 2 (B) a 11 x 1 + a 12 x 2 = b 1 a 21 + c a 11 x 1 + a 22 + c a 12 x 2 = b 2 + c b 1
In the 2 × 2 linear systems that follow, the system (B) is obtained from (A) by performing the elementary operation E 2 + c E 1 . Prove that any solution, x 1 = s 1 , x 2 = s 2 , for (A) is a solution for (B). Similarly, prove that any solution, x 1 = t 1 , x 2 = t 2 , for (B) is a solution for (A). (A) a 11 x 1 + a 12 x 2 = b 1 a 21 x 1 + a 22 x 2 = b 2 (B) a 11 x 1 + a 12 x 2 = b 1 a 21 + c a 11 x 1 + a 22 + c a 12 x 2 = b 2 + c b 1
Solution Summary: The author demonstrates that any solution, x_1=s2 is also a solution for (B) in the following (2times 2) linear system
In the
2
×
2
linear systems that follow, the system (B) is obtained from (A) by performing the elementary operation
E
2
+
c
E
1
. Prove that any solution,
x
1
=
s
1
,
x
2
=
s
2
, for (A) is a solution for (B). Similarly, prove that any solution,
x
1
=
t
1
,
x
2
=
t
2
, for (B) is a solution for (A).
(A)
a
11
x
1
+
a
12
x
2
=
b
1
a
21
x
1
+
a
22
x
2
=
b
2
(B)
a
11
x
1
+
a
12
x
2
=
b
1
a
21
+
c
a
11
x
1
+
a
22
+
c
a
12
x
2
=
b
2
+
c
b
1
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