The system of equations may have a unique solution, an infinite number of soluti

Question

The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the system, if a solution exist. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answers in terms of z as in Example 3) {2x + y - z = 3 x - y + 2z = 3 x + y - z = 2 (x, y, z) = 0, 7, 5 Use technology to solve the system of equations, if a solution exists. (If there are infinitely many solutions, express your answers in terms of x_4 and x_5 as in Example 3. If there is no solution, enter NO SOLUTION) {x_1 + 3x_2 + 4x_3 - x_4 + 2x_5 = 1 x_1 - x_2 - 2x_3 + x4 = 3 x_1 + 2x_2 + 3x_3 + x_4 + 4x_5 = 0 2x_1 + 3x_2 + 2x_3 + 2x_ 5 = 4 (x_1, x_2, x_3, x_4, x_5) = (1 - 2x_4 - 3x_5, 4 + 5x4 + 7x_5, -3 - 3x_4 - 5x_5)

Explanation / Answer

Add 2 and 3 and subtract from 1 we have:

y-2z = -2....(4)

Now, subbing in equation 2 we have:

x+2=3
x=1

y-z = 1...(5)

We use the above and (4) to solve:

z = 3
y = 4

(So, x,y,z,is 1,4,3)

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