Solutions to quiz 5

A = {{2,-2,3,5},{1,-4,5,1},{0,3,-2,1}};
B = {{1,0,3,0},{0,2,4,0},{0,1,1,0},{1,1,0,4}};

Transpose[A]//MatrixForm

Det[B]

B//MatrixForm

Lets do  a cofactor matrix....  How about Problem 4(f) on page 157....

A = {{1,3,0},{-4,16,3},{0,-3,-5}};

A//MatrixForm

CC = {{0,0,0},{0,0,0},{0,0,0}};

CC[[1,1]] = (-1)^(1+1)*Det[A[[{2,3},{2,3}]]]

CC[[1,2]] = (-1)^(1+2)*Det[A[[{2,3},{1,3}]]]

CC[[1,3]] = (-1)^(1+3)*Det[A[[{2,3},{1,2}]]]

CC[[2,1]] = (-1)^(2+1)*Det[A[[{1,3},{2,3}]]]

CC[[2,2]] = (-1)^(2+2)*Det[A[[{1,3},{1,3}]]]

CC[[2,3]] = (-1)^(2+3)*Det[A[[{1,3},{1,2}]]]

CC[[3,1]] = (-1)^(3+1)*Det[A[[{1,2},{2,3}]]]

CC[[3,2]] = (-1)^(3+2)*Det[A[[{1,2},{1,3}]]]

CC[[3,3]] = (-1)^(3+3)*Det[A[[{1,2},{1,2}]]]

CC//MatrixForm

AInv = 1/Det[A]*Transpose[CC];

AInv//MatrixForm

A.AInv//MatrixForm

AInv.A//MatrixForm

Inverse[A]//MatrixForm

Minors[A]//MatrixForm

CC//MatrixForm

Minor