Question

Consider the following system of equations:
x
1 3x
2 x
3 = 3
x
1 + 5x
2 + 3x
3 = 1
x
1 + 7x
2 + 3x
3 = 1
Check whether the system of equations have a solution or not

Answer 1

Answer on Question #46090 – Math – Linear Algebra

Task:

Consider the following system of equations:

$$\left\{ \begin{array}{l} x _ {1} + 3 x _ {2} + x _ {3} = 3 \\ x _ {1} + 5 x _ {2} + 3 x _ {3} = 1 \\ x _ {1} + 7 x _ {2} + 3 x _ {3} = 1 \end{array} \right.$$

Check whether the system of equations have a solution or not

Solution:

The system of equations is nonhomogeneous, it has a solution, when $|A| \neq 0$ :

$$| A | = \left| \begin{array}{ccc} 1 & 3 & 1 \\ 1 & 5 & 3 \\ 1 & 7 & 3 \end{array} \right| = (5 * 3 - 3 * 7) - (3 - 3) + (7 - 5) = 4 \neq 0.$$

So the system of equations has a solution.

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