document.write( "Question 389009: Please help me solve this problem.\r
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document.write( "What is the value of the game represented by the following matrix: \r
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document.write( "5 1 2
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document.write( "8 0 -4
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document.write( "4 1 3
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Algebra.Com's Answer #275479 by haileytucki(390)![]() ![]() You can put this solution on YOUR website! Finding the determinant:\r \n" ); document.write( "\n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]\r \n" ); document.write( "\n" ); document.write( "Setup the determinant by breaking it into smaller components. \n" ); document.write( "-(1)M[D,8,-4:4,3]+0M[D,5,2:4,3]-(1)M[D,5,2:8,-4]\r \n" ); document.write( "\n" ); document.write( "The determinant of a 2x2 matrix can be found using the formula M[D,a,b:c,d]=ad-cb \n" ); document.write( "-(1)((8)(3)-(4)(-4))+0M[D,5,2:4,3]-(1)M[D,5,2:8,-4]\r \n" ); document.write( "\n" ); document.write( "Simplify the determinant. \n" ); document.write( "-40+0M[D,5,2:4,3]-(1)M[D,5,2:8,-4]\r \n" ); document.write( "\n" ); document.write( "Since the matrix is multiplied by 0, the determinant is 0. \n" ); document.write( "-40+0-(1)M[D,5,2:8,-4]\r \n" ); document.write( "\n" ); document.write( "The determinant of a 2x2 matrix can be found using the formula M[D,a,b:c,d]=ad-cb \n" ); document.write( "-40+0-(1)((5)(-4)-(8)(2))\r \n" ); document.write( "\n" ); document.write( "Simplify the determinant. \n" ); document.write( "-40+0+36\r \n" ); document.write( "\n" ); document.write( "Simplify the expression. \n" ); document.write( "Answer= -4\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Or.....if you want to trapose the matrix:\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]\r \n" ); document.write( "\n" ); document.write( "Transpose the matrix by moving element 0,0 in the original matrix to element 0,0 in the transposed matrix. \n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]->M[5,1,1:1,1,1:1,1,1]\r \n" ); document.write( "\n" ); document.write( "Transpose the matrix by moving element 0,1 in the original matrix to element 1,0 in the transposed matrix. \n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]->M[5,1,1:1,1,1:1,1,1]\r \n" ); document.write( "\n" ); document.write( "Transpose the matrix by moving element 0,2 in the original matrix to element 2,0 in the transposed matrix. \n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]->M[5,1,1:1,1,1:2,1,1]\r \n" ); document.write( "\n" ); document.write( "Transpose the matrix by moving element 1,0 in the original matrix to element 0,1 in the transposed matrix. \n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]->M[5,8,1:1,1,1:2,1,1]\r \n" ); document.write( "\n" ); document.write( "Transpose the matrix by moving element 1,1 in the original matrix to element 1,1 in the transposed matrix. \n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]->M[5,8,1:1,0,1:2,1,1]\r \n" ); document.write( "\n" ); document.write( "Transpose the matrix by moving element 1,2 in the original matrix to element 2,1 in the transposed matrix. \n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]->M[5,8,1:1,0,1:2,-4,1]\r \n" ); document.write( "\n" ); document.write( "Transpose the matrix by moving element 2,0 in the original matrix to element 0,2 in the transposed matrix. \n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]->M[5,8,4:1,0,1:2,-4,1]\r \n" ); document.write( "\n" ); document.write( "Transpose the matrix by moving element 2,1 in the original matrix to element 1,2 in the transposed matrix. \n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]->M[5,8,4:1,0,1:2,-4,1]\r \n" ); document.write( "\n" ); document.write( "Transpose the matrix by moving element 2,2 in the original matrix to element 2,2 in the transposed matrix. \n" ); document.write( "M[5,1,2:8,0,-4:4,1,3]->M[5,8,4:1,0,1:2,-4,3]\r \n" ); document.write( "\n" ); document.write( "Transpose the matrix by turning all rows in original matrix to columns in the transposed matrix. \n" ); document.write( "M[5,8,4:1,0,1:2,-4,3] ( The : represents the split in the column )\r \n" ); document.write( "\n" ); document.write( "I added this, but I believe that you were looking for the answer within the first solution above (determinant) \n" ); document.write( " |