Prev: Calculating the age of a person
Next: building matrix with diffrent rows length
From: naser on 14 Feb 2010 03:53
I have a equation AX=0; which A is parametric. First I solved det(A)=0 and then I use null(A) to give me X. But when I use subs() function and then use null(A), reply is 3 column and it is not true.
Would you please help me.

syms x
A=[1 1 0 0;2 3 4 0;cos(x) cosh(x) 0 1;sin(x) sinh(x) 1 1];
y=det(A)
reply:
y=4*cos(x) - 4*cosh(x) - 4*sin(x) + 4*sinh(x) - 1

Now
f=@(x) 4*cos(x) - 4*cosh(x) - 4*sin(x) + 4*sinh(x) - 1;
[x1]=fzero(@f,[37:38])
A=[1 1 0 0;2 3 4 0;cos(x1) cosh(x1) 0 1;sin(x1) sinh(x1) 1 1];
null(A)

reply:

x1 =
37.4299477502371

ans =
-0.453742676394043 -0.891132753083832 0
6.70505820727308e-017 9.34410358043419e-018 -1.11022302462514e-016
-0.891132753083832 0.453742676394043 9.4209430227917e-017
8.39531089254629e-017 -4.27468390131729e-017 1
From: John D'Errico on 14 Feb 2010 05:32
"naser " <naser.sepehry(a)gmail.com> wrote in message <hl8dlh$t5q$1(a)fred.mathworks.com>...
> I have a equation AX=0; which A is parametric. First I solved det(A)=0 and then I use null(A) to give me X. But when I use subs() function and then use null(A), reply is 3 column and it is not true.
> Would you please help me.
>
> syms x
> A=[1 1 0 0;2 3 4 0;cos(x) cosh(x) 0 1;sin(x) sinh(x) 1 1];
> y=det(A)
> reply:
> y=4*cos(x) - 4*cosh(x) - 4*sin(x) + 4*sinh(x) - 1
>
> Now
> f=@(x) 4*cos(x) - 4*cosh(x) - 4*sin(x) + 4*sinh(x) - 1;
> [x1]=fzero(@f,[37:38])
> A=[1 1 0 0;2 3 4 0;cos(x1) cosh(x1) 0 1;sin(x1) sinh(x1) 1 1];
> null(A)
>
> reply:
>
> x1 =
> 37.4299477502371
>
> ans =
> -0.453742676394043 -0.891132753083832 0
> 6.70505820727308e-017 9.34410358043419e-018 -1.11022302462514e-016
> -0.891132753083832 0.453742676394043 9.4209430227917e-017
> 8.39531089254629e-017 -4.27468390131729e-017 1

First of all, be very careful here. You are running
into numerical problems, computing sinh(x) and
cosh(x) when x is as large as 37.

x = 37.4299477502371;

sinh(x)
ans =
9.00719925474113e+15

cosh(x)
ans =
9.00719925474113e+15

Worse, then you are applying null to the resulting
matrix. The linear algebra is failing you here, as the
result is garbage.

Don't just throw big numbers at a computer and
not think about what you are doing. You will
numerical garbage.

John
 | 
Pages: 1
Prev: Calculating the age of a person
Next: building matrix with diffrent rows length