মধ্য সমানুপাতী নির্ণয় করাে : abc,
aC
b
|
Answers
Answer:
Example 2: Use Cramer’s Rule to solve
−x + 3y − 2z = 5
4x − y − 3z = −8
2x + 2y − 5z = 7
.
Step 1: Find the determinant, D, by using the x, y, and z values from the problem.
4 6 −60
D = |
−1 3 −2
4 −1 −3
2 2 −5
| = |
−1 3 −2
4 −1 −3
2 2 −5
|
−1 3
4 −1
2 2
= −39 − (−50) = 11
−5 −18 −16
Step 2: Find the determinant, Dx, by replacing the x-values in the first column with the values
after the equal sign leaving the y and z columns unchanged.
14 −30 120
Dx = |
5 3 −2
−8 −1 −3
7 2 −5
| = |
5 3 −2
−8 −1 −3
7 2 −5
|
5 3
−8 −1
7 2
= −6 − 104 = −110
25 −63 32
Step 3: Find the determinant, Dy, by replacing the y-values in the second column with the
values after the equal sign leaving the x and z columns unchanged.
32 21 −100
Dy = |
−1 5 −2
4 −8 −3
2 7 −5
| = |
−1 5 −2
4 −8 −3
2 7 −5
|
−1 5
4 −8
2 7
= −126 − (−47) = −79
−40 −30 −56
Step 4: Find the determinant, Dz, by replacing the z-values in the third column with the values
after the equal sign leaving the x and y columns unchanged.
−10 16 84
Dz = |
−1 3 5
4 −1 −8
2 2 7
| = |
−1 3 5
4 −1 −8
2 2 7
|
−1 3
4 −1
2 2
= −1 − 90 = −91
7 −48 40
Step 5: Use Cramer’s Rule to find the values of x, y, and z.
x =
Dx
D
=
−110
11 = −10
y =
Dy
D
=
−79
11 = −
79
11
z =
Dz
D
=
−91
11 = −
91
11
Answer written as on order triple: (−10, −
79
11
, −
91
11)