[quote=googoogaga;72360]Hello, could I please receive some assistance in the solving of the following homework problem. My answer does not math the book's. Thanks! Here it is...

Evaluate the determinant of the following 4 by 4 matrix

2 1 2 1

3 0 1 1

-1 2 -2 1

-3 2 3 1

Book's answer: 20 (How?)

My answer: -23

2 1 2 1

3 0 1 1 <-- i chose this row to cross out and then cross out each column

-1 2 -2 1 with each corresponding entry in that row and take det times that

-3 2 3 1 entry

3 * det[] + 0 ( zero times det of 3X3 = 0) + det[] + det[]

1 2 1 2 1 1 2 1 2

2 -2 1 2 -2 1 -1 2 1 match the colors

2 3 1 -3 2 1 -3 2 1

then 3 * the det of that 3X3 matrix by choosing a row to do the same as before then you are left with two by twos. then add the det of the second and then the third.

3*{det[]+2*det[]+det[]} + {2*det[]+det[]+det[]} + {2*det[]+det[]+2*det[]}

-2 1 2 1 2 -2 2 1 -1 1 -1 2 2 -2 -1 -2 -1 2

3 1 2 1 2 3 2 1 -3 1 -3 2 2 3 -3 3 -3 2

det of 2X2 upper left times lower right minus lower left times upper right (-2*1)-(3*1)

3(-5+0+2) + (0+2+8) + (20+-9+8)

-9 + 10 + 19 = 20

or if you have a ti-82 or above just go to 2nd matrix then edit and insert the 4X4 matrix then quit then 2nd matrix again and go down to det( enter and then 2nd matrix again and select A B C or whatever slot you entered that matrix in and voila.

hope the colors helped can't get the numbers to line up like a want it would be easier to show that way