Question

Given the row-reduced form of the matrix corresponding to the system of equations found in part (b.), state the solution as a point. Use the parameter t if necessary. [1 0 0; 0 1 0; -2 3 0; 0 60 0] (x, y, z) = ()

Answer 1

To solve the matrix, you should approach each row as an individual equation, solve the equation, and get the values of (x, y, z).

We take each row and arrange them in the form of equations as follows:
- First row: 1x + 0y + 0z = 0 --> x = 0.
- Second row: 0x + 1y + 0z = 0 --> y = 0.
- Third row: -2x + 3y = 0 --> after substituting x = 0 and y = 0, we see that this equation doesn't provide us any extra information.
- Fourth row: 0x + 60y + 0z = 0 --> after substituting x = 0 and y = 0, we also see that the fourth row doesn’t give us information on value of z.

But we still need a value for z. Since neither the third nor the fourth row provided us with a value or equation for z, we introduce a parameter, which we'll write as symbol 't'. So we can conclude that z = t.

Synthesizing the results we found, the ordered triple that solves the system of equations represented by the given matrix is (x, y, z) = (0, 0, t). And this is the solution for the original matrix equation.