9*8*7 / (9 over 3)
regarding part B
we choose 2 floors from 3 (3 over 2)
we have three person the first has 6 places the second has 5 third is 4
correct?
(3 over 2)*6*5*4 /(9 over 3)
correct?
in a three floor building on each store we have 3 appartments.
so in total we have 9 appartments.
every appartment has one person.
3 people enter the elevator(from the entrace of th building),each one goes to the floor he lives in.
A)
what are the odds that the elevator will stop at...
\left(\begin{array}{cc}14 & 13\\13 & 14\end{array}\right)
the caracterstic polinomial
P(t)=(t-14)^{2}-169=t^{2}-28t+27
t=1 t=27
for t=1 i get (-1,1) and for t=27 i got the same (-1,1)
so the transformation matrices is not invertible which is wrong
where is my mistake?
find B matrices so B^{3}=A=\left(\begin{array}{cc}14 & 13\\13 & 14\end{array}\right)
,the diagonal form of A is D=\left(\begin{array}{cc}a & 0\\0 & b\end{array}\right)
i got weird numbers so for convinience the eigenvalues are a,b
so there is U for which...
8)
U=\{x=(x_{1},x_{2},x_{3},x_{4})\in R^{4}|x_{1}+x_{2}+x_{4}=0\}
is a subspace of R^{4}
v=(2,0,0,1)\in R^{4}
find u_{0}\in U so ||u_{0}-v||<||u-v||
how i tried:
U=sp\{(-1,1,0,0),(-1,0,0,1),(0,0,1,0)\}
i know that the only u_{0} for which this innequality will work
is if it will be the...
7)
T:R^{2}->R^{2} projection transformation on X-axes parallel to the
line
y=-\sqrt{3}x
find the representative matrices of T{*} by B=\{(1,0),(0,1)\} basis
how i tried:
i understood that the x axes stayed the same but the y axes turned
into
y=-\sqrt{3}x
our T takes some vector and...
6)there is normal T in unitarian final space.
v\neq0,v\in V prove that if \{sp(v)\}^{\perp} is T variant then
v is eigenvector of T
?
hint:prove that T*(v) is orthogonal to \{sp(v)\}^{\perp}
what i have done:
suppose u\in\{sp(v)\}^{\perp}
we take the definition of T*
(Tu,v)=(u,T*v)...
4)
A=\left(\begin{array}{cc}4 & -4\\1 & 0\end{array}\right)
find the jordan form and the transformation matrices P to this jordan
form.
the caracteristic and minimal polinomial is P(t)=M(t)=(t-2)^{2}
so the jordan form is J_{A}=\left(\begin{array}{cc}2 & 1\\0 & 2\end{array}\right).
my prof...
3)
q:R^{3}->R is defined by q(x,y,z)=4(xy+yz+zx)
find the minimal M\in R so q(x,y,z)\leq M(x^{2}+y^{2}+z^{2})
?
why in the solution the calculate the caracteristic polinomial
?
why if (t+2) is in power 2 then we have -2 in two members of
the formula q(v) ??
our polinomial doesn't...
1)
q(x_{1,}x_{2,}x_{3})=
x_{1}^{2}+5x_{2}^{2}+26x_{3}^{2}+2x_{1}x_{2}+10x_{1}x_{3}+6x_{2}x_{3}
V=\{x=(x1,x2,x3)\in R^{3}:q(x)=0\}
check if V is a subspace of R^{3} and
find the basis of V?
how i tried:
i diagonolized it the representative by rows and columns and i see
that
q is...
i need to show that there is x1 f(x1)<c
f(x2)>c
from the limit when x goes to sero we get zero -e<f(x)<e
from the limit when x goes minus infinity f(x)<-N
what e to chhose?
what N to choose?
i need to prove that \frac{1}{\sqrt{x}} is not uniformly continues in (0,1)
for epsilon=0.5
|\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{y}}|=|]\frac{\sqrt{y}-\sqrt{x}}{\sqrt{xy}}\frac{\sqrt{y}+\sqrt{x}}{\sqrt {y}+\sqrt{x}}|=|\frac{y-x}{(\sqrt{y}-\sqrt{x})\sqrt{xy}}|...