er the Toiowing imatrix and two vectors 13140 1 2 6 3 91 1 1 -3 0 -31 -2 (-2-61-53-3
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Er the Toiowing imatrix and two vectors 13140 1 2 6 3 91 1 1 -3 0 -31 -2 (-2-61-53-3
1. If the vectors and are orthogonal with respect to the weighted inner product < >...
1. If the vectors
and
are orthogonal with respect to the weighted inner
product
<
> =
, what must be true about the weights
?
2. Do there exist scalars k and m such that the vectors p1 =
2+kx+6, p2 =
m+5x+3 and
p3 = 1 + 2x + 3 are mutually
orthogonal with respect to the standard inner product on P2?
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Let be an orthonormal set of a Hilbert space. Let and be two vectors in H....
Let
be an orthonormal set of a Hilbert space. Let
and
be two vectors in H. Show that
converges absolutely, and that
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Let X(t) = 2; if 0 t 1; 3; if 1 t 3; -5; if 3 t 4: or in one formula X(t) = 2I[0;1](t) + 3I...
Let X(t) =
2; if 0 t 1;
3; if 1 t 3;
-5; if 3 t 4:
or in one formula X(t) = 2I[0;1](t) +
3I(1;3](t) -
5I(3;4](t).
Give the Itˆo integral
X(t)dB(t)
as a sum of random variables, give its distribution,
specify the mean and the variance.
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Consider the following three vectors in ; v1 = (1, 7, −2), v2 = (4, 3,...
Consider the following three vectors in
; v1 = (1, 7, −2), v2 = (4, 3, 5), v3 = (2, −11, 9):
i) Say whether v1, v2, v3 are linearly dependent or linearly
independent. (Justify)
ii) Say if v1, v2, v3 generate
. (justify)
iii) If it exists, determine the constants c1, c2, c3, such that
c1v1 + c2v2 + c3v3 = (0, −5, 13/5), or argue why it cannot be
written as a linear combination.
We were unable to...
1/v (Sec/uM) -8 -6 -2 1 1 2 3 4 5 6 7 8 0 1/[S]...
1/v (Sec/uM) -8 -6 -2 1 1 2 3 4 5 6 7 8 0 1/[S] (UM-1) We were unable to transcribe this image
1 Fund I I- Jund is,,s, V 6. AMA 18A 12R IN 3 2r 12M er...
1 Fund I I- Jund is,,s, V 6. AMA 18A 12R IN 3 2r 12M er 20n nd te ale, voges , 57 4ic MUM 3A 12V +h We were unable to transcribe this image
Let S ⊆ be the tetrahedron having vertices (0, 0, 0), (0, 1, 1), (1, 2,...
Let S ⊆
be the tetrahedron having vertices (0, 0, 0), (0, 1, 1), (1, 2,
3), and (−1, 0, 1).
Let f :
→
be the function defined by f(x, y, x) = x − 2y + 3z.
Using the change of variables theorem,
rewrite
as an integral over a 3-rectangle, then use Fubini’s theorem to
evaluate the integral.
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Two vectors: Find the magnitude and direction for the resultant vector The magnitude R = The...
Two vectors:
Find the magnitude and direction for the resultant vector
The magnitude R =
The Direction =
Write your answer as integers
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Wave function: Quantum Mechanical Hamonic Osculator, n=0, 1, 2, 3. Prove the following equation...
Wave function: Quantum Mechanical Hamonic Osculator, n=0, 1, 2,
3.
Prove the following equation is true:
(reduced mass)
of ac 0 2. 乙 4万 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
of ac 0 2. 乙 4万
13 -1 -3 61 A= 0 0 -3 6 . Find all the vectors mapped to...
13 -1 -3 61 A= 0 0 -3 6 . Find all the vectors mapped to the zero vector by x → Ax. Is the map 16 -2 -5 10] TA(x) = Ax one-to-one (injective)? e le vert is the vector b= 3 in range(TA)? What about c= 13 ? Is L7 sector what aboute=p} L7 Ta onto (surjective)?
1. If the vectors
and
are orthogonal with respect to the weighted inner
product
<
> =
, what must be true about the weights
?
2. Do there exist scalars k and m such that the vectors p1 =
2+kx+6, p2 =
m+5x+3 and
p3 = 1 + 2x + 3 are mutually
orthogonal with respect to the standard inner product on P2?
N 12 We were unable to transcribe this image= 1211 + Աշշ W1, W2 We were...
Let
be an orthonormal set of a Hilbert space. Let
and
be two vectors in H. Show that
converges absolutely, and that
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let X(t) =
2; if 0 t 1;
3; if 1 t 3;
-5; if 3 t 4:
or in one formula X(t) = 2I[0;1](t) +
3I(1;3](t) -
5I(3;4](t).
Give the Itˆo integral
X(t)dB(t)
as a sum of random variables, give its distribution,
specify the mean and the variance.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
Consider the following three vectors in
; v1 = (1, 7, −2), v2 = (4, 3, 5), v3 = (2, −11, 9):
i) Say whether v1, v2, v3 are linearly dependent or linearly
independent. (Justify)
ii) Say if v1, v2, v3 generate
. (justify)
iii) If it exists, determine the constants c1, c2, c3, such that
c1v1 + c2v2 + c3v3 = (0, −5, 13/5), or argue why it cannot be
written as a linear combination.
We were unable to...
1/v (Sec/uM) -8 -6 -2 1 1 2 3 4 5 6 7 8 0 1/[S] (UM-1) We were unable to transcribe this image
1 Fund I I- Jund is,,s, V 6. AMA 18A 12R IN 3 2r 12M er 20n nd te ale, voges , 57 4ic MUM 3A 12V +h We were unable to transcribe this image
Let S ⊆
be the tetrahedron having vertices (0, 0, 0), (0, 1, 1), (1, 2,
3), and (−1, 0, 1).
Let f :
→
be the function defined by f(x, y, x) = x − 2y + 3z.
Using the change of variables theorem,
rewrite
as an integral over a 3-rectangle, then use Fubini’s theorem to
evaluate the integral.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image}
Two vectors:
Find the magnitude and direction for the resultant vector
The magnitude R =
The Direction =
Write your answer as integers
A=4 Ñ +7 B= 8 -29 We were unable to transcribe this imageWe were unable to transcribe this image
Wave function: Quantum Mechanical Hamonic Osculator, n=0, 1, 2,
3.
Prove the following equation is true:
(reduced mass)
of ac 0 2. 乙 4万 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
of ac 0 2. 乙 4万
13 -1 -3 61 A= 0 0 -3 6 . Find all the vectors mapped to the zero vector by x → Ax. Is the map 16 -2 -5 10] TA(x) = Ax one-to-one (injective)? e le vert is the vector b= 3 in range(TA)? What about c= 13 ? Is L7 sector what aboute=p} L7 Ta onto (surjective)?
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