- #1

- 2,264

- 316

- Homework Statement
- 1. Find a linear equation in the variables x, y and z that has a general solution:

x = 3 - 4p + q

y = p

z = q

where p and q are arbitrary parameters

2. Express a general solution for the equation in part (1) in two other different ways

3. Write down a linear system of two different non zero linear equations such that the system has the same general solution as in part (1)

- Relevant Equations
- Not sure

1)

x = 3 - 4p + q

x = 3 - 4y + z

x + 4y - z = 3

2) x + 4y - z = 3

(i) let x = a and y = b, so z = a + 4b - 3

General solution:

x = a

y = b

z = a+ 4b - 3

(ii) let x = r and z = t, so y = (3 - r + t) / 4

General solution:

x = r

y = (3 - r + t) / 4

z = t3) I don't understand this part. Is the answer the same as part (1)? Can I just take random equations like x +2y = 1 and 2y - z = 2? Is this the form asked by the questions?

Thanks

x = 3 - 4p + q

x = 3 - 4y + z

x + 4y - z = 3

2) x + 4y - z = 3

(i) let x = a and y = b, so z = a + 4b - 3

General solution:

x = a

y = b

z = a+ 4b - 3

(ii) let x = r and z = t, so y = (3 - r + t) / 4

General solution:

x = r

y = (3 - r + t) / 4

z = t3) I don't understand this part. Is the answer the same as part (1)? Can I just take random equations like x +2y = 1 and 2y - z = 2? Is this the form asked by the questions?

Thanks