Solve the following system of equations and give a geometrical interpretation of the result.
x + y + z = 6
2x + y − 3z = -5
4x − 5y + z = −3
Give a geometrical interpretation of the intersection of the planes with equations
x + y − 3 = 0
y + z + 5 = 0
x + z + 2 = 0
Determine a scalar equation for the plane that passes through the point (2, 0, −1) and is perpendicular to the line of intersection of the planes
2x + y – z + 5 = 0 and x + y + 2z + 7 = 0.
Here's the system.
...(1)
...(2)
...(3)
Now looking at (1)
Now we substitute where we see into both (2) and (3) giving
...(2)
...(3)
Neatening this up gives
...(2)
...(3)
Grouping like terms
...(2)
...(3)
Do you follow? Can you use this method again on (2) and (3) to finish it?
isn't it easier to do determinant of matrix ? so u can see how many there are (if any) solutions of the system and so it's much easier to understand the geometrical interpretation
how do the planes correspond between them, how do they (if they are) intersects, is it in one point or is it along the line or... and so on