i. Let U1 be the set of solutions for the equation For which values of a and b is U1 a subspace of R4? ii. Let U2 be the set of solutions for the equation For which values of a and b is U2 a subspace of R4? iii. Let U3 be the set of solutions for the equation For which values of a and b is Us a subspace of R4? Justify your answer in each case b) Let V be the set of solutions for the set of equations x2-3T3 ах 1 For which values of a, bE R is V a subspace of R4? Use part (a) or otherwise to justify your answer.
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4. (a) L ,DER et a i. Let U1 be the set of solutions for the equation For which values of a and b is U1 a subspace of R4? ii. Let U2 be the set of solutions for the equation For which values of a and...
1. Let S = {(a, b, c, d) e R4: a+b+c= 0} a). Show that S...
1. Let S = {(a, b, c, d) e R4: a+b+c= 0} a). Show that S is a subspace of R4. b). Find a basis of S. 2. Let M = {(ui, uz, u3) € R3: U1 + U2 = 2). Is Ma subspace of R3? Explain your answer, if your answer is yes, give a proof why it is a subspace. If your answer is no, then show why it is not a subspace.
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector...
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector space. (b) Prove that L is an affine subspace of R3 (c) Compute a vector v such that L = v + W
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y...
I am looking for how to explain #4 part b. I have gotten the matrix A...
I am looking for how to explain #4 part b. I have gotten the
matrix A and I believe the answer is W = span{ v1 u2 u3 } however
I'm not really sure if that is correct or not. Please give a small
explanation. Also im not sure if I need to represent the vectors in
A as columns or rows, or if either one works.
For the next two problems, W is the subspace of R4 given by...
4. Let A be a 4 x 4 matrix with determinant 7. Which of the following...
4. Let A be a 4 x 4 matrix with determinant 7. Which of the following statements are correct? Justify your answer. (a) For some vector b € R4, the system of equations AT = 5 has exactly one solution. (b) For some vector 5 € R4, the system of equations Az = 5 has infinitely many solutions. (c) For some vector b E R4, the system of equations Az = has no solution. (d) For all vectors be R4,...
Let (,)j-0,n-1 be an arbitrary set of n integer-valued coordinates Hence the values of rj and...
Let (,)j-0,n-1 be an arbitrary set of n integer-valued coordinates Hence the values of rj and y are integers In this question, we deine the bounding rectangle as follows 1. The rectangle has horizontal and vertical edges. 2. It is the smallest rectangle which encloses all the points (Fj, yi), j = 0, ,n-1. 3. Let the coordinates of the bounding rectangle be (uo, vo), (ui,vi), (u2, 2) and (us, vs) (u0,t0) = botton left corner (u1, v)bom right corner...
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 sta...
Hi,
could you post solutions to the following questions. Thanks.
2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
a 0 0 where a b, and c are positive numbers. Let S be the unit ball whose bounding surface has the equation x-x R3 + R3...
a 0 0 where a b, and c are positive numbers. Let S be the unit ball whose bounding surface has the equation x-x R3 + R3 be a linear transformation determined by the matrix A= 1 Complete Let 0 b 0 + x 0 0 c parts a and b below. u1 x1 2 ,2 2 a Show that T S is bounded by the ellipsoid with the equation 1 Create a vector u = that is within set...
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u...
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u - (1,0,1,0), u2 = (0.-1, 1.0), and ug = (0.0, 1,-1). Use the Gram-Schmidt process to transform the basis (uj, u, uz) into an orthonormal basi (A) v1 = (-12,0, 2.0), v2 - (VG VG VG, o), v3 - (I ) (B) v1 = (-V2.0, .), v2 - (VG VG VG o), v3 - (™J - V3 VI-V3) (C) v1 - ($2.0, 92.0), v2...
Hi! i only need help with #4. for part ii) the equation we are suppsed to...
Hi! i only need help with #4. for part ii) the equation we are
suppsed to use is: I=1/2E(sum)CiZi^2.
for part iii. the equation we are suppose to use:
logYi=-0509zi^2I^1/2.
for part iv) the equations we are suppsed to use are: 1. Ecell
~ Ecell ^o -(RT/nF) lnQ. 2.
Q=(Yc[C])^c(YD[D])^d/(YA[A]^a(Yb[B])^b
Thank you!!:)
Pre-Lab Questions If I wish to construct a Voltaic Cell using Zinc-Zinc Ion and Silver-Silver Ion Half- Cells, which metal will serve as the Anode and which the...
(7) Let V = {ui, U2 . . . . Un} with n > 4. In...
(7) Let V = {ui, U2 . . . . Un} with n > 4. In this exercise we will compute the probability that in a random graph with vertex set V we have that v and v2 have an edge between them or have an edge to a common vertex (i.e, have a common neighbour) (If you are troubled by my use of the term random we choose a graph on n vertices uniformly at random from the set...
1. Let S = {(a, b, c, d) e R4: a+b+c= 0} a). Show that S is a subspace of R4. b). Find a basis of S. 2. Let M = {(ui, uz, u3) € R3: U1 + U2 = 2). Is Ma subspace of R3? Explain your answer, if your answer is yes, give a proof why it is a subspace. If your answer is no, then show why it is not a subspace.
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector space. (b) Prove that L is an affine subspace of R3 (c) Compute a vector v such that L = v + W
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y...
I am looking for how to explain #4 part b. I have gotten the
matrix A and I believe the answer is W = span{ v1 u2 u3 } however
I'm not really sure if that is correct or not. Please give a small
explanation. Also im not sure if I need to represent the vectors in
A as columns or rows, or if either one works.
For the next two problems, W is the subspace of R4 given by...
4. Let A be a 4 x 4 matrix with determinant 7. Which of the following statements are correct? Justify your answer. (a) For some vector b € R4, the system of equations AT = 5 has exactly one solution. (b) For some vector 5 € R4, the system of equations Az = 5 has infinitely many solutions. (c) For some vector b E R4, the system of equations Az = has no solution. (d) For all vectors be R4,...
Let (,)j-0,n-1 be an arbitrary set of n integer-valued coordinates Hence the values of rj and y are integers In this question, we deine the bounding rectangle as follows 1. The rectangle has horizontal and vertical edges. 2. It is the smallest rectangle which encloses all the points (Fj, yi), j = 0, ,n-1. 3. Let the coordinates of the bounding rectangle be (uo, vo), (ui,vi), (u2, 2) and (us, vs) (u0,t0) = botton left corner (u1, v)bom right corner...
Hi,
could you post solutions to the following questions. Thanks.
2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
a 0 0 where a b, and c are positive numbers. Let S be the unit ball whose bounding surface has the equation x-x R3 + R3 be a linear transformation determined by the matrix A= 1 Complete Let 0 b 0 + x 0 0 c parts a and b below. u1 x1 2 ,2 2 a Show that T S is bounded by the ellipsoid with the equation 1 Create a vector u = that is within set...
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u - (1,0,1,0), u2 = (0.-1, 1.0), and ug = (0.0, 1,-1). Use the Gram-Schmidt process to transform the basis (uj, u, uz) into an orthonormal basi (A) v1 = (-12,0, 2.0), v2 - (VG VG VG, o), v3 - (I ) (B) v1 = (-V2.0, .), v2 - (VG VG VG o), v3 - (™J - V3 VI-V3) (C) v1 - ($2.0, 92.0), v2...
Hi! i only need help with #4. for part ii) the equation we are
suppsed to use is: I=1/2E(sum)CiZi^2.
for part iii. the equation we are suppose to use:
logYi=-0509zi^2I^1/2.
for part iv) the equations we are suppsed to use are: 1. Ecell
~ Ecell ^o -(RT/nF) lnQ. 2.
Q=(Yc[C])^c(YD[D])^d/(YA[A]^a(Yb[B])^b
Thank you!!:)
Pre-Lab Questions If I wish to construct a Voltaic Cell using Zinc-Zinc Ion and Silver-Silver Ion Half- Cells, which metal will serve as the Anode and which the...
(7) Let V = {ui, U2 . . . . Un} with n > 4. In this exercise we will compute the probability that in a random graph with vertex set V we have that v and v2 have an edge between them or have an edge to a common vertex (i.e, have a common neighbour) (If you are troubled by my use of the term random we choose a graph on n vertices uniformly at random from the set...
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