equations by using cramer's rule 5x-6y+4z=15,7x+4y-3z=19,2x+y+6z=46
Answers
Answer:
Answer
The above equations can be written in matrix form as
⎣
⎢
⎢
⎡
5
7
2
;−6
;6
;1
;4
;−3
;6
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
15
19
46
⎦
⎥
⎥
⎤
or AX = B
|A| = D =
∣
∣
∣
∣
∣
∣
∣
∣
5
7
2
;−6
;4
;1
;4
;−3
;6
∣
∣
∣
∣
∣
∣
∣
∣
Apply C
1
−2C
2
,C
3
−6C
2
to make two zeros in R
3
D=
∣
∣
∣
∣
∣
∣
∣
∣
17
−1
0
;−6
;4
;1
;40
;−27
;0
∣
∣
∣
∣
∣
∣
∣
∣
=−
∣
∣
∣
∣
∣
∣
17
−1
;40
;−27
∣
∣
∣
∣
∣
∣
=−[−459+40]=419
=0.
∴ The matrix A is non-singular or rank of matrix A is
3. We will have a unique solution and the equations are consistent.
By Crammer's rule
D
1
x
=
D
2
y
=
D
3
z
=
D
1
Where D
1
is obtained from D by replacing the first column of D by b's i.e. 15,19,46
D
1
=
∣
∣
∣
∣
∣
∣
∣
∣
15
19
46
;−6
;4
;1
;4
;−3
;6
∣
∣
∣
∣
∣
∣
∣
∣
=15(27)−19(−40)+46(2)=1257
∴
1257
x
=
1676
y
=
2514
z
=
419
1
∴x=3,y=4,z=6.