RIJEÃ…Â ENI ZADACI IZ MATEMATIKE
RIJEÃ…Â ENI ZADACI IZ MATEMATIKE
RIJEÃ…Â ENI ZADACI IZ MATEMATIKE
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18. Riješite sustav,Rješenje:3x + y + 2z − 2w = 03x + 2y − z + 3w = −42x − y + 2z − w = −2⎡⎤ ⎡⎤3 1 2 −2 | 0 2 −1 2 −1 | −2⎣3 2 −1 3 | −4⎦ ∼ ⎣3 2 −1 3 | −4⎦ ∼2 −1 2 −1 | −2 3 1 2 −2 | 0⎡1 − 1 21 − 1 ⎤ ⎡2| −1 1 − 1 21 − 1 ⎤2| −1∼ ⎣3 2 −1 3 | −4⎦ ∼ ⎣ 7902−42| −1⎦ ∼53 1 2 −2 | 0 02−1 − 1 2| 3⎡1 − 1 21 − 1 ⎤ ⎡3 12| −1 1 0∼ ⎣0 1 − 8 97 7| − 2 7 7| − 8 ⎤7⎦7∼ ⎣0 1 − 8 9502−1 − 1 7 7| − 2 ⎦7∼132| 3 0 07− 26 267|7⎡3 11 07 7| − 8 ⎤ ⎡⎤71 0 0 1 | −2∼ ⎣0 1 − 8 97 7| − 2 ⎦7∼ ⎣0 1 0 −1 | 2 ⎦0 0 1 −2 | 2 0 0 1 −2 | 2x + w = −2y − w = 2z − 2w = 2x = −2 − wy = 2 + wz = 2 + 2ww ∈ R19
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