3.3 a) MatrixRank[{{1,-8,3},{2,1,1},{4,7,-4}}] c) MatrixRank[{{0,2,-4},{-1,-4,5},{3,1,7},{0,5,-10},{2,3,0}}] 3.5 b) LinearSolve[{{2,-1}, {0,0}}, {2,3}] f) LinearSolve[{{0,1,0}, {1,0,0},{0,0,1}}, {-3,0,2}] g) Solve[{{1,4,0,0,3}, {0,0,1,0,-2},{0,0,0,1,2}}.{{x},{y},{z},{u},{v}} == {{2}, {0},{4}}] 3.6 d) solve x+2y-z-3u+4v=2, 2x-y+3z+2u-v=4, x+4y+2z-5u+3v=6, x+15y+6z-19u+9v=2 3.7 b) solve x+2y+3z=0, 3x-5y-2z=0, x+3y+4z=0, 2x-3y-z=0, 5x+y+6z=0 f) solve x+2y+3z=4, 5x+4y+z=13, 3x+3y+2z=10 g) solve x+2u-3v=5,2x+2y+2z-u+4v=0, x-y-z+u-v=3, y+z+u-2v=2 i) solve x+2y+3z+u=0, x-2y+z+u=0, 3x-3y-7u=0, 4y+2z+5u=0 3.8 c) solve Determinant[{{2,-a,1},{4,-2,a},{6,-4,3}}]=0 solve 2x-(4/3)*y+z=0, 4x-2y+(4/3)*z=0, 6x-4y+3z=0 solve 2x-(2)*y+z=0, 4x-2y+(2)*z=0, 6x-4y+3z=0 e) solve Determinant[{{2,1,-1,0},{1,1,2,-1},{0,a,1,2}, {-1,2,1,1}}]=0 solve 2x+y-z=4, x+y+2z-w=4, (5)*y+z+2w=0, -x+2y+z+w=-4 3.9 b) solve Determinant[{{4,1,1},{-8,2,-1}, {4,-1,a}}]=0 solve 4x+y+z=0, -8x+2y-z=0, 4x-y+(1/2)z=0