how do you find the value of x in this matrix equation?

Question

2    4    4

2    x    -10   =740

-5   9    3

Answer 1

I assume that the equation says that the determinant of the 3x3 matrix with an unknown, x, as the center element is equal to 740.  To solve for x, work out the value of the determinant (which will depend on x) and set it equal to 740.

 

There are several ways of working out the value of the determinant.  The method of co-factors is one.  However,  a "stripping" method works well for a 3x3 matrix.  We  will have three terms with +1 factor and three with a -1 factor.  Call the 3x3 matrix M.   Then

 

det(M) =  (6 x + 72 + 200)  -  (-20 x -180 +24) =  26 x  + 428      Setting this equal to 740  gives

 

26 x + 428 =  740      with the solution  x =  12

Answer 2

I think this is a determinant equation, not a matrix equation.

(2)(x)(3) + (4)(-10)(-5) + (4)(2)(9)
- [(2)(-10)(9) + (4)(2)(3) + (4)(x)(-5)] = 740

6x + 200 + 72 - [-180 + 24 -20x] = 740

26x + 272 + 180 - 24 = 740

26x + 72 + 80 - 24 = 440

26x + 2 + 60 - 4 = 370

26x + 58 = 370

26x + 8 = 320

26x = 312

13x = 156

x = 12

check:

GeoGebra results:
http://www.wyzant.com/resources/files/262409/determinant