Transcription of DETERMINANTS BY ROW AND COLUMN EXPANSION
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DETERMINANTS BY ROW AND COLUMN EXPANSION
DETERMINANTS BY ROW AND COLUMN EXPANSIONTERRY A. LORING1. EXPANDING ALONG AROW ORCOLUMNThe book does a good job explaining how you can expand on a the can expand on any COLUMN or row. You use a checkerboard pattern tofigure the signs:+ + + ++ + + +and the cross out a row and a columns, several times, to write the big determi-nant as a sum/difference of many (many) smaller , see the ANEXAMPLELet s computedet(A)in several ways, whereA= 0 1 4 323 1 4 406 0 2 323 1 6 60 12 TERRY A. on the second row (twice). 0 1 4 323 1 4 406 0 2 323 1 6 60 = 3 X0 1 4 32X3X1X4X4X0X6 0 2 32X3 1 6 60 + 0X1 4 32X3X1X4X4X06X0 2 323X1 6 60 4 0 1X4 32X3X1X4X4X06 0X2 323 1X6 60 +40 0 1 4X3X2X3X1X4 4XX06 0 2X1X323 1 6X6X0 = 3 1 4 320 2 321 6 60 + 0 4 326 2 323 6 60 4 0 1 326 0 323 1 60 +40 0 1 46 0 23 1 6 = 3 2 1X4 32X0X1X1X61X6 60 32 1 4X3X2X0X1X1X61 6X6XX0 + 6 X0 4 32X3X1X1X6X3 6 60 +2 0X4 32X3X1X1X63X6 60 32 0 4X3X2X3X1X1X63 6X6X0 4 6 X0 1 32X3X0X1X6X3 1
2 TERRY A. LORING 2.1. Expand on the second row (twice). 0 1 4 32 3 1 4 40 6 0 2 32 3 1 6 60 = −3 X0 1 4 32 X3 X1 X4 X4X0 X6 0 2 32
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