MULTIPLY 5A+3B+C WITH 2C
Answers
Step-by-step explanation:
Put the coefficients in a augmented matrix:
a
−
3
b
+
2
c
=
−
1
→
[
1
−
3
2
∣
−
1
]
5
a
+
3
b
+
c
=
−
5
→
[
1
−
3
2
∣
−
1
5
3
1
∣
−
5
]
14
a
−
2
b
+
3
c
=
6
→
⎡
⎢
⎣
1
−
3
2
∣
−
1
5
3
1
∣
−
5
14
−
2
3
∣
6
⎤
⎥
⎦
Perform row operations, until you get an identity matrix:
⎡
⎢
⎣
1
−
3
2
∣
−
1
5
3
1
∣
−
5
14
−
2
3
∣
6
⎤
⎥
⎦
Multiply row 1 by -5 and add to row 2:
⎡
⎢
⎣
1
−
3
2
∣
−
1
0
18
−
9
∣
0
14
−
2
3
∣
6
⎤
⎥
⎦
Multiply row 1 by -14 and add to row 2:
⎡
⎢
⎣
1
−
3
2
∣
−
1
0
18
−
9
∣
0
0
40
−
25
∣
20
⎤
⎥
⎦
Divide row 2 by 9 and row 3 by 5:
⎡
⎢
⎣
1
−
3
2
∣
−
1
0
2
−
1
∣
0
0
8
−
5
∣
4
⎤
⎥
⎦
Multiply row 2 by -4 and add to row 3:
⎡
⎢
⎣
1
−
3
2
∣
−
1
0
2
−
1
∣
0
0
0
−
1
∣
4
⎤
⎥
⎦
Multiply row 3 by -1 and leave it that way after adding to row 2:
⎡
⎢
⎣
1
−
3
2
∣
−
1
0
2
0
∣
−
4
0
0
1
∣
−
4
⎤
⎥
⎦
Divide row 3 by 2:
⎡
⎢
⎣
1
−
3
2
∣
−
1
0
1
0
∣
−
2
0
0
1
∣
−
4
⎤
⎥
⎦
Multiply row 3 by -2 and add to row 1:
⎡
⎢
⎣
1
−
3
0
∣
7
0
1
0
∣
−
2
0
0
1
∣
−
4
⎤
⎥
⎦
Multiply row 2 by 3 and add to row 1:
⎡
⎢
⎣
1
0
0
∣
1
0
1
0
∣
−
2
0
0
1
∣
−
4
⎤
⎥
⎦
The identity matrix says,
a
=
1
,
b
=
−
2
,
and
c
=
−
4
Check:
1
−
3
(
−
2
)
+
2
(
−
4
)
=
−
1
5
(
1
)
+
3
(
−
2
)
+
−
4
=
−
5
14
(
1
)
−
2
(
−
2
)
+
3
(
−
4
)
=
6
−
1
=
−
1
−
5
=
−
5
6
=
6
Step-by-step explanation: