SOLUTION: Please help me solve this problem. What is the value of the game represented by the following matrix: 5 1 2 8 0 -4 4 1 3

Question 389009: Please help me solve this problem.

What is the value of the game represented by the following matrix:
5 1 2
8 0 -4
4 1 3

Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
Finding the determinant:
M[5,1,2:8,0,-4:4,1,3]
Setup the determinant by breaking it into smaller components.
-(1)M[D,8,-4:4,3]+0M[D,5,2:4,3]-(1)M[D,5,2:8,-4]
The determinant of a 2x2 matrix can be found using the formula M[D,a,b:c,d]=ad-cb
-(1)((8)(3)-(4)(-4))+0M[D,5,2:4,3]-(1)M[D,5,2:8,-4]
Simplify the determinant.
-40+0M[D,5,2:4,3]-(1)M[D,5,2:8,-4]
Since the matrix is multiplied by 0, the determinant is 0.
-40+0-(1)M[D,5,2:8,-4]
The determinant of a 2x2 matrix can be found using the formula M[D,a,b:c,d]=ad-cb
-40+0-(1)((5)(-4)-(8)(2))
Simplify the determinant.
-40+0+36
Simplify the expression.
Answer= -4

Or.....if you want to trapose the matrix:

M[5,1,2:8,0,-4:4,1,3]
Transpose the matrix by moving element 0,0 in the original matrix to element 0,0 in the transposed matrix.
M[5,1,2:8,0,-4:4,1,3]->M[5,1,1:1,1,1:1,1,1]
Transpose the matrix by moving element 0,1 in the original matrix to element 1,0 in the transposed matrix.
M[5,1,2:8,0,-4:4,1,3]->M[5,1,1:1,1,1:1,1,1]
Transpose the matrix by moving element 0,2 in the original matrix to element 2,0 in the transposed matrix.
M[5,1,2:8,0,-4:4,1,3]->M[5,1,1:1,1,1:2,1,1]
Transpose the matrix by moving element 1,0 in the original matrix to element 0,1 in the transposed matrix.
M[5,1,2:8,0,-4:4,1,3]->M[5,8,1:1,1,1:2,1,1]
Transpose the matrix by moving element 1,1 in the original matrix to element 1,1 in the transposed matrix.
M[5,1,2:8,0,-4:4,1,3]->M[5,8,1:1,0,1:2,1,1]
Transpose the matrix by moving element 1,2 in the original matrix to element 2,1 in the transposed matrix.
M[5,1,2:8,0,-4:4,1,3]->M[5,8,1:1,0,1:2,-4,1]
Transpose the matrix by moving element 2,0 in the original matrix to element 0,2 in the transposed matrix.
M[5,1,2:8,0,-4:4,1,3]->M[5,8,4:1,0,1:2,-4,1]
Transpose the matrix by moving element 2,1 in the original matrix to element 1,2 in the transposed matrix.
M[5,1,2:8,0,-4:4,1,3]->M[5,8,4:1,0,1:2,-4,1]
Transpose the matrix by moving element 2,2 in the original matrix to element 2,2 in the transposed matrix.
M[5,1,2:8,0,-4:4,1,3]->M[5,8,4:1,0,1:2,-4,3]
Transpose the matrix by turning all rows in original matrix to columns in the transposed matrix.
M[5,8,4:1,0,1:2,-4,3] ( The : represents the split in the column )
I added this, but I believe that you were looking for the answer within the first solution above (determinant)
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