Graphics Programs Reference
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It checks!
Problem 4
[x, y, z] = solve('3*x - 9*y + 8*z = 2', '2*x - 3*y + 7*z = -
1','x-6*y+z=3','x', 'y', 'z')
x=
39/5*y+22/5
y=
y
z=
-9/5*y-7/5
We get a one-parameter family of answers depending on the variable
y
.In
fact the three planes determined by the three linear equations are not
independent, because the first equation is the sum of the second and third.
The locus of points that satisfy the three equations is not a point, the
intersection of three independent planes, but rather a line, the intersection
of two distinct planes. Once again we check.
B = [3, -9, 8; 2, -3, 7; 1, -6, 1]; B*[x; y; z]
ans =
[]
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Problem 5
syms x y; factor(xˆ4 - yˆ4)
ans =
(x-y)*(x+y)*(x^2+y^2)
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