SOLUTION: This question is from my College Algebra Class Notes and Work Guide. It deals with Cramer's Rule. {-3 4 -4} {-3 K -1} = 58 {1 4 -2} The numbers in the braquet, a

Algebra ->  Matrices-and-determiminant -> SOLUTION: This question is from my College Algebra Class Notes and Work Guide. It deals with Cramer's Rule. {-3 4 -4} {-3 K -1} = 58 {1 4 -2} The numbers in the braquet, a      Log On


   

Question 135889: This question is from my College Algebra Class Notes and Work Guide. It deals with Cramer's Rule.
{-3 4 -4}
{-3 K -1} = 58
{1 4 -2}

The numbers in the braquet, are all in one large bracket and then they all equal 58. I'm just not sure where to do with it.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
{-3 4 -4}
{-3 K -1} = 58
{1 4 -2}
--------------------
The left side is a determinant.
You are evaluate the determinant; set it equal to 58; solve for K.
---------------------
Determinant Value: [-3*K*-2+-3*4*-4 + 1*-1*4]
-[-4*K*1 + -1*4*-3 + -2*-3*4] =58
= [6K+48-4] - [-4K+12+24] = 58
= 10K+8 = 58
10K = 50
K= 5
===============
Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I suspect you are supposed to solve for K.

%28matrix%283%2C3%2C-3%2C4%2C-4%2C-3%2CK%2C-1%2C1%2C4%2C-2%29%29=58

To calculate the value of a 3X3 determinant, create a 5X3 matrix by repeating the first two columns to the left of the original 3

%28matrix%283%2C5%2C-3%2C4%2C-4%2C-3%2C4%2C-3%2CK%2C-1%2C-3%2CK%2C1%2C4%2C-2%2C1%2C4%29%29

Next you perform the following calculation:


The three complete 3-factor diagonal products down right summed minus the three complete 3-factor diagonal products up right summed.

In your case:



You can check the arithmetic yourself, but it reduces to 10K%2B8, but you were given that the determinant = 58, so:

10K%2B8=58
10K=50
K=5