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aud50
27.02.2020 •
Mathematics
Show that there do not exist scalars c1, c2, and c3 such that c1(1, 0, 1, 0) + c2(1, 0, -2, 1) + c3(2, 0, 1, 2) = (1, -2, 2, 3)
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Ответ:
Write the system in augmented-matrix form:
Row reduce this matrix:
Add -1(row 1) to row 3:![\left[\begin{array}{ccc|c}1&1&2&1\\0&0&0&-2\\0&-3&-1&1\\0&1&2&3\end{array}\right]](/tpl/images/0527/0547/0fed8.png)
Add 3(row 4) to row 3:![\left[\begin{array}{ccc|c}1&1&2&1\\0&0&0&-2\\0&0&5&10\\0&1&2&3\end{array}\right]](/tpl/images/0527/0547/48a62.png)
Multiply row 3 by 1/5:![\left[\begin{array}{ccc|c}1&1&2&1\\0&0&0&-2\\0&0&1&2\\0&1&2&3\end{array}\right]](/tpl/images/0527/0547/4c757.png)
Add -2(row 3) to row 4:![\left[\begin{array}{ccc|c}1&1&2&1\\0&0&0&-2\\0&0&1&2\\0&1&0&-1\end{array}\right]](/tpl/images/0527/0547/85114.png)
Add -2(row 3) and -1(row 4) to row 1:This matrix tells us that
,
, and
, but clearly
, so there is no solution.
Ответ:
because that is the answer