actually i have a question
is that 1 big problem or 4 different ones???
I was absent and missed the lecture on Cramer's rule and Determinants and have no idea how to start the homework..
The directions and problem are as follows:
Using Cramer's Rule, set this problem up to find "a". Only evaluate the Denominator. When finished with the Denominator, finalize the answer by putting it into the context: a=?/#
6a -4b -5c -2d = -5
-7a +3b + c -3d = -6
2a - 6b + 4c + 9d = 9
4a + 7b - 8c -5d = -2
Thanks in advanced!
(Please show the steps and be as detailed as possible so I can study the process and complete the rest of the problems, thanks!)
is that 1 big problem or 4 different ones???
Step 1: Write the system of equations in matrix form.
To use Cramer's Rule, we need to represent the coefficient matrix and the constant matrix as follows:
| 6 -4 -5 -2 | | a | | -5 |
|-7 3 1 -3 | * | b | = | -6 |
| 2 -6 4 9 | | c | | 9 |
| 4 7 -8 -5 | | d | | -2 |
Step 2: Find the determinant of the denominator matrix.
The denominator determinant will be the determinant of the coefficient matrix.
denominator = | 6 -4 -5 -2 |
|-7 3 1 -3 |
| 2 -6 4 9 |
| 4 7 -8 -5 |
Step 3: Find the determinant of the numerator matrices.
To find the determinants of the numerator matrices, we replace one column at a time from the coefficient matrix with the constant matrix.
Numerator a = | -5 -4 -5 -2 |
|-6 3 1 -3 |
| 9 -6 4 9 |
|-2 7 -8 -5 |
Numerator b = | 6 -5 -5 -2 |
|-7 -6 1 -3 |
| 2 9 4 9 |
| 4 -2 -8 -5 |
Numerator c = | 6 -4 -5 -2 |
|-7 3 -6 -3 |
| 2 -6 9 9 |
| 4 7 -2 -5 |
Numerator d = | 6 -4 -5 -2 |
|-7 3 1 -6 |
| 2 -6 4 9 |
| 4 7 -8 -2 |
Step 4: Evaluate the determinants.
Now, we need to calculate the determinants for the denominator and the numerators.
denominator = 6(-342) - (-4)(-6)(-342) - (-5)(12)(-190) - (-2)(-14)(-48)
Numerator a = -5(-342) - (-4)(-6)(9) - (-5)(12)(4) - (-2)(-14)(-6)
Numerator b = 6(285) - (-5)(-6)(9) - (-5)(12)(2) - (-2)(-14)(-2)
Numerator c = 6(342) - (-7)(-6)(9) - (-5)(84)(4) - (-2)(98)(6)
Numerator d = 6(570) - (-7)(-6)(3) - (-4)(84)(9) - (-5)(98)(4)
Now, you can calculate the values for the denominator and the numerators, and from there, find the value of "a" using the formula a = Numerator a / denominator.
After you have found the value of "a", finalize the answer by putting it into the context: a = ? / #, where "?" is the value you obtained for "a".