Bằng định thức, giải các hệ phương trình sau:
a)
\(\left\{ \matrix{
5x - 4y = 3 \hfill \cr
7x - 9y = 8 \hfill \cr} \right.\)
b)
\(\left\{ \matrix{
\sqrt 3 x + \sqrt 2 y = - 1 \hfill \cr
2\sqrt 2 x + \sqrt 3 y = 0 \hfill \cr} \right.\)
a) Ta có:
\(D = \left| \matrix{
5\,\,\,\, - 4 \hfill \cr
7\,\,\,\, - 9 \hfill \cr} \right| = - 45 + 28 = - 17\)
\({D_x} = \left| \matrix{
3\,\,\,\,\,\, - 4 \hfill \cr
8\,\,\,\,\,\, - 9 \hfill \cr} \right| = - 27 + 32 = 5\)
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\({D_y} = \left| \matrix{
5\,\,\,\,\,\,\,3 \hfill \cr
7\,\,\,\,\,\,8 \hfill \cr} \right| = 40 - 21 = 19\)
Hệ có nghiệm:
\(\left\{ \matrix{
x = {{{D_x}} \over D} = {{ - 5} \over {17}} \hfill \cr
y = {{{D_y}} \over D} = - {{19} \over {17}} \hfill \cr} \right.\)
b) Ta có:
\(D = \left| \matrix{
\sqrt 3 \,\,\,\,\,\,\,\sqrt 2 \hfill \cr
2\sqrt 2 \,\,\,\,\sqrt 3 \hfill \cr} \right| = 3 - 4 = - 1\)
\({D_x} = \left| \matrix{
- 1\,\,\,\,\,\,\sqrt 2 \hfill \cr
0\,\,\,\,\,\,\,\,\,\sqrt 3 \hfill \cr} \right| = - \sqrt 3 \)
\({D_y} = \left| \matrix{
\sqrt 3 \,\,\,\,\,\, - 1 \hfill \cr
2\sqrt 2 \,\,\,\,\,\,0 \hfill \cr} \right| = 2\sqrt 2 \)
Hệ có nghiệm duy nhất:
\(\left\{ \matrix{
x = {{{D_x}} \over D} = \sqrt 3 \hfill \cr
y = {{{D_y}} \over D} = - 2\sqrt 2 \hfill \cr} \right.\)