CHƯƠNG 2
BÀI TẬP HỆ PHƯƠNG TRÌNH TUYẾN TÍNH
I. Giả hệ phương trình bậc 3    2x x 2x x x x  1 − 2 + x3 = 12  1 − 2 − 3 = 4  1 + x x 2 + 2 3 = −12    a) x x x 1 + 6x2 b) c) − 3 = 2 3x1 + 4x2 − 2x3 = 11 2x1 − 2 + 2x3 = 2    3x x 1 + x2 + 8x3 = 16 3x1  − 2x2 + 4x3 = 11 4x1 + x2 + 4 3 = −2   3x x x  1 + 2x2 + x3 = 5  1 + 2x2 + 4 3 = 31   d) 2x1 + 3x2 + x3 = 1 e) 5x1 + x2 + 2x3 = 29   2x  x 1 + x2 + 3x3 = 11 3x1 − 2 + x3 = 10
II. Giả hệ phương trình bậc 4   x x x x 1 − 2x x 2 + 3 3 − 4x4 = 4 1 − 2 + 2x3 − 3 4 = 1        x x x x x x 2 3 + 4 =  1 + 4 2 3 a) − −3 b) − − 2x4 = −2 x x x x x x  1 + 3 2 − 4 = 1  1 − 4 2 + 3x3 − 2 4 = −2      x x −7x2 + 3x3 + 3x4 = −3 1 − 8x2 + 5x3 − 2 4 = −2 3  x x x x x 1 + 4 2 + 5 3 + 7x4 = 1 3 1 + x2 − 3 3 + x4 = 1       2x x x x 1 + 6x2 2 1 − 2 + 7x3 − 3 4 = 2 c) − 3x3 + 4x4 = 2 d) 4x x x x x x  1 + 2 2 + 13 3 + 10x4 = 0  1 + 3x2 − 2 3 + 5 4 = 3     5x  x x 1 + 21x3 + 13x4 = 3 3x1 − 2 2 + 7x3 − 5 4 = 3 x x x  x x 1 + 2 2 + 3x3 − 2 4 = 6 2x x 1 − 2 + 2 3 + 2 4 = 4       2x x x x x x x 1  − 2 2 − 2 3 − 3 4 = 8 3x1 + 3 2 + 3 3 + 2 4 = 6 e) f) 3x 3x x x  1 + 2x x 2 − 3 + 2x4 = 4  1 − 2 − 3 + 2x4 = 6     2x x x  1 − 3 2 + 2 3 + x4 = −8 3x x 1 − 2 + 3x x 3 − 4 = 6
III. Giải và biện luận hệ phương trình   (a + 1)x ax  1 + x2 + x3 = 1  1 + x x 2 + 3 + x4 = 1   a) x x x x x 1 + (a + 1) 2 + 3 = a b) 1 + ax2 + 3 + x4 = a   x x x x x 1 + 2 + (a + 1) 3 = a2 1 + 2 + ax a 3 + x4 = 2   x x x 1 − 2 + ax3 − 4 = a 2x1 + 3x2 + x3 + x4 = 3       x x x x x x 1 + ax2 3 + 4 = 4x1 + 6 2 + 3 3 + 4 4 = 5 c) − −1 d) ax ax x x 6x x x x  1 + 2 − 3 − 4 = −1  1 + 9 2 + 5 3 + 6 4 = 7     x x x a  x x 1 + 2 + 3 + x4 = − 8x1 + 12 2 + 7 3 + tx4 = 9 1   tx x x x 1 + x x x 2 + 3 + 4 = 1 1 + 2 + 3 + mx4 = 1       x x x x 1 + tx2 + x3 + 4 = 1  1 + mx2 + x3 + 4 = 1 e) f) x mx  1 + x x 2 + tx3 + 4 = 1  1 + x x 2 + 3 + x4 = 1     x  x x x 1 + x x 2 + 3 + tx4 = 1 1 + 2 + mx3 + 4 = 1
IV. Giải hệ phương trình x x x x x  x 1 + 2 + 3 + 4 + 5 = 7 2x1 + x x 2 − 3 − 4 + x5 = 1       3x x x x x x x x 1 + 2x2 + 3 + 4 − 3 5 =  1 a) −2 b) − 2 + 3 + x4 − 2 5 = 0 x x x 3x x 1 + 3x2 − 3  2 + 2 3 + 2x4 + 6 5 = 23  3 − 3x4 + 4x5 = 2     5x x x x  x x x 1 + 4 2 + 3 3 + 3x4 − 5 = 12
4 1 + 5x2 − 5 3 − 5 4 + 7x5 = 3 2x1 − 2x2 + x x 3 − 4 + x5 = 1    x x x x 1 + 2 2 c) − 3 + x4 − 2 5 = 1 4x x 1 − 10x2 + 5x3 − 5  4 + 7x5 = 2   2x x x
1 − 14x2 + 7x3 − 7 4 + 11 5 = −1 V. Giải hệ phương trình 2x  1 + x2 + 4x3 + 7x4 = 0  a) 4x x 1 + 2x2 − 7 3 + 5x4 = 0  x x x x 1 − 2 2 + 5 3 − 3 4 = 0 5x x 1 + 4x2 − 2 3 + x4 + 6x5 = 0    2x x x 1 + 2x x 2 4 5 = 0 b) − 3 + 4 + 3 2x x x  1 + 2x x 2 − 3 + 4 4 + 3 5 = 2   7x x x x
1 + 6x2 − 3 3 + 3 4 + 9 5 = 0 (x1 + 2x x 2 c) − 3 3 + 6x4 = 0 2x x 1 − 2 + 7x3 + 4x4 = 0 (x x x 1 + 2x2 + x3 + 2 4 + 3 5 = 0 d) 2x x x 1 + 4x2 + x3 + 3 4 + 4 5 = 0 2