Graphics Reference
In-Depth Information
the polynomial first derivative of a is:
>> pretty(poly2sym(polyder(a)))
5 4 3 2
12 x - 20 x + 20 x + 24 x
the polynomial first derivative of the product of
a
and
b
is:
>> pretty(poly2sym(polyder(a,b)))
9 8 7 6 5 4 3 2
-140 x + 522 x - 760 x + 301 x + 432 x + 300 x + 356 x + 45 x + 12
the polynomial quotient
a/b
will be
q/d
where
q
and
d
are:
>> [q,d]=polyder(a,b);
>> pretty(poly2sym(q))
9 8 7 6 5 4 3 2
-28 x + 118 x - 120 x + 251 x - 192 x + 180 x + 220 x - 45 x -12
>> pretty(poly2sym(d))
8 7 6 5 4 2
49 x - 210 x + 225 x - 168 x + 360 x + 144 x
eXerCISe 6-2
Find the characteristic polynomial of the matrix whose rows are vectors [2, -4, 5, 8], [0, 0, 0, 1], [-7, 15, 0.12]
and [0, -1, -1, 0]. also find the roots of this polynomial and check that the matrix satisfies the equation of your
characteristic polynomial.
>> A=[2,-4,5,8;0,0,0,1;-7,15,0,12;0,-1,-1,0]
A =
2 -4 5 8
0 0 0 1
-7 15 0 12
0 -1 -1 0
>> p=poly(A)
p =
1.0000 -2.0000 48.0000 -67.0000 33.0000
