Joseph

I'm having real trouble understanding matrices and how to solve the questions associated with them, ie:

Consider the following two 2 × 2 matrices:

A =

1 2

2 3

and B =

2 0

−2 −5

Find by hand A−1BT +2I and (2A + BT)−1, and verify that

(A−1BT + 2I)−1 = (2A + BT)−1A

by evaluating both sides of the equation.

Any help would be appreciated a lot!

This is what I have so far.

clear

x = -2:.01:4;

y = x.^2-2*x-4;

y=originlen(x);

plot(x,y)

pause % Press any key to continue

x1=input('Enter left hand endpoint of subinterval: ');

x2=input('Enter right hand endpoint of subinterval: ');

xmin = fminbnd('originlen',x1,x2)

ymin=originlen(xmin);

originlen is this

function d=originlen(x)

x=-2:0.01:4;

d=sqrt(x.^2+(x.^2-2*x-4).^2);

plot(x,d)

This is currently the error that I'm getting:

??? Operands to the and && operators must be convertible to logical scalar values.

Error in ==> fminbnd at 260 if ( (abs(p)<abs(0.5*q*r)) && (p>q*(a-xf)) && (p<q*(b-xf)) )

Error in ==> plotting at 12 xmin = fminbnd('originlen',x1,x2)

What I want the program to do is display the point on the parabola that is closest to the origin, (found by d(x)), and the minimum distance.

Currently I have this.

x = [1, .1, .01, .001, .0001, .00001, .000001, .0000001, .00000001, .000000001, .0000000001, .00000000001];

f = 0;

e = 2.71828;

for i = 1:length(x);

f = (e.^(x).*sin(x)/x).^2

end

Now I want it to display f for every single value of X, not just the end result. What am I doing wrong?

f(x) = (e^2x − (e^x * cos x)^2)/x^2 and g(x) = (e^x *sin x /x)^2, all for x =/= 0.

I'm having trouble showing algebraically that f(x) = g(x) for all x =/= 0. Any help would be appreciated.

I'm trying to plot x2 +9y2 = 36 in MATLAB, but it just doesn't want to work, even if I split it up to

1/3sqrt(36 − x2) and −1/3sqrt(36 − x2)

Can someone please help me?

I'm trying to find a recursive sequence from the question listed below:

At the beginning of week 1 of a certain calendar year, a suburban park has an area of

10,000 square metres affected by weeds. Soon after the beginning of week n, for n = 1, 2, 3... the local council eradicates weeds from 700n/(n + 1) square metres of the affected area at the cost of 20 cents per square metre. However, during each week, the weeds spread so that the area of the park affected by weeds increases by 5%. Let an denote the area (in square metres) of the park affected by weeds at the start of week n for n ≥ 1, and let cn denote the total cumulative cost (in dollars) of eradicating the weeds up to the beginning of week n for n ≥ 1.

So far, I've found the rule for the nth term is

tn = (10000-(700n/(n + 1))x(1.05)^n

The first four terms are:

n1 = 10132.5

n2 = 10510.5

n3 = 10968.5

n4 = 11304.2

I'm having a lot of trouble finding a recursive definition though, some help would be greatly appreciated. :)

Find, showing all working, a recursive definition of the sequence with general term

tn = 5(n + 1)!/4n, n ≥ 1.

That's my question, and I've figured out the first five terms and I've figured out that the formula simplifies every time to a common thing, but I can't figure out the formula. Could someone help me find it please, even just set me on the right track?

I cut off the sensitive pulp on the top of my finger a month ago at work, and my doctor has just said that I'm fit to return to pre-injury duties. Now I've done a bit of reading and I've read that it's possible I may get a payout as the damage is permanent, and my finger will forever be scarred and damaged because of the injury. There is no nerve damage, and a mm of bone was removed. Will I get a payout do you think, or because it's just flesh will nothing happen?

Also while I'm here, if I leave my current job, will a payout still be possible?

I live in Australia, but I'm happy to see answers from other countries as well to see the procedure there.

Long story short, had the tip of my finger cut off and skin was grafted from my hand to my finger. Had about 19 stitches in in total. The stitches are out now (since yesterday), and I want to keep the bandage on my finger, but can I take the bandage off my hand now the stitches are out, or do I need to keep it on to continue the healing process?