Solve the system ⎧⎩⎨⎪⎪⎪⎪⎪⎪4x1−x13x1−3x1−5x2+x2−4x2+3x2+4x3+2x3+6x3+6x3+4x4=+3x4=+7x4=+9x4=3143

Mathematics

1 answer:

ad-work [718]4 years ago

7 0

It appears you have the system with augmented matrxi ...

$\left[\begin{array}{cccc|c}4&-5&4&4&3\\-1&1&2&3&1\\3&-4&6&7&4\\-3&3&6&9&3\end{array}\right]$

Right away, you notice that the 4th row is 3 times the 2nd row, so the equations are dependent and will not have a unique solution.

My calculator tells me the reduced equations can be written

... x1 -14x3 -19x4 = -8

... x2 -12x3 -16x4 = -7

This says there are two dependent equations in the set, not just one.

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katovenus [111]

To write the any polynomial in standard form you must first put it in terms separated only by $+,-$ operators, then you must order terms $x^n$ descendingly according to $n$ . In your case $-\frac{1}{5}x^2$ will be the first term because it has highest power, followed by $-8x^1$ and $+7x^0$ .