Solve using Determinants and Cramer's Rule?
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!)
actually i have a question
is that 1 big problem or 4 different ones???
that is one big problem haha
I DON'T GET THE MINUSES IN THIS ONE? PLEASE HELP????
To solve the given system of equations using Cramer's Rule, we need to find the value of "a" by evaluating the denominator determinant. Let's go step by step:
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".