Homework Answers
We used definition of subspace of vector space and neccessary and sufficient conditions of subspace.
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2. In each of the following find out if the subset S is a subspace of...
1 point) Let V R2 and let H be the subset of V of all points...
1 point) Let V R2 and let H be the subset of V of all points on the line-4x-3y-0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? | H does not contain the zero vector of V | 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and...
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2]...
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x +...
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x + x, 1-2x2} be a subset of P2, Is s is abasis for P2? 2 1 3 0 uestion (6) Let A=12 1 a) Compute the determinant of the matrix A via reduction to triangular form. (perform elementary row operations)
Question (7) Consider...
Determine whether the given set S is a subspace of the vector space V.
Determine whether the given set S is a subspace of
the vector space V.A. V=C2(ℝ) (twice continuously
differentiable functions), and S is the subset of VV consisting of
those functions satisfying the differential equation
y″=0. B. V=ℙ5, and SS is the subset of ℙ5 consisting of those polynomials satisfying
p(1)>p(0)C. V=ℙ4, and SS is the subset of ℙ4 consisting of all polynomials of the form
p(x)=ax3+bx.D. V=Mn×n(ℝ), and SS is the subset of all
symmetric matrices.E. V=ℝ2, and S consists of...
please can you give the solutions not just anwsers. Thank you. 1 LetE CR E :...
please can you give the solutions not just anwsers. Thank
you.
1 LetE CR E : x + x2 - X3 = 1, be an affine subspace. Select one or more: 1. The affine subspace ECR is passing through the point (0,3,2) il E = aff((1,0,0), (2,0,1),(1, 1, 1)) l. The affine subspace H CR' perpendicular to E and passing through the point (1,2,3) is given by H -(1,2,3) + lin((3,3, -3)) W. The Image of the affine orthogonal projection...
linear algebra 2 parts mcq part a part b Solve the system 5 = ;3x -...
linear algebra 2 parts mcq
part a
part b
Solve the system 5 = ;3x - ܕܠ ܐ2 + X1 13 = 3xa - ܕ2xn + X -X+ X2 ܂3 1 xto tec b. Xt tec SE N 51 0 d. XS ܢܬ ܝ ܝ SEC e X=S <. [ f. x=s H Let be the set of third degree polynomials H = {ax + ax? + ax | AEC} Is H a subspace of ? Why or why not?...
3. Is each of the following is a subspace of R4? If yes, find a basis A. The set of all (x1, z2, s, z4) that satisf...
3. Is each of the following is a subspace of R4? If yes, find a basis A. The set of all (x1, z2, s, z4) that satisfy both 2x1-32 o 51 +22 30 B. The set of all (x1,22, z3, z4) that satisfy both 5x1+22 3 0
3. Is each of the following is a subspace of R4? If yes, find a basis A. The set of all (x1, z2, s, z4) that satisfy both 2x1-32 o 51 +22 30...
(1 point) Determine whether the given set S is a subspace of the vector space V....
(1 point) Determine whether the given set S is a subspace of the vector space V. A. V = R", and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed mxn matrix. B. V is the vector space of all real-valued functions defined on the interval (-oo, oo), and S is the subset of V consisting of those functions satisfying f(0) 0 C. V Mn (R), and S is the...
Find a subset of S which is a basis of the vector space V. (a) V...
Find a subset of S which is a basis of the vector space V. (a) V = R3, S = = {(!),()()($).():(})} (b) V = P3(R), S = {1+ 2x, 1 + x + x2, 2+x - x2, 3+2x, * - 2x3}
a. Let W and X both be subspaces of a vector space V. Prove that dim(WnX)...
a. Let W and X both be subspaces of a vector space V. Prove that dim(WnX) > dim(W) + dim(X) - dim(V) b. Define a plane in R" (as a vector space) to be any subspace of dimension 2, and a line to be any subspace of dimension 1. Show that the intersection of any two planes in R' contains a line. c. Must the intersection of two planes in R* contain a line?
1 point) Let V R2 and let H be the subset of V of all points on the line-4x-3y-0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? | H does not contain the zero vector of V | 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and...
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x + x, 1-2x2} be a subset of P2, Is s is abasis for P2? 2 1 3 0 uestion (6) Let A=12 1 a) Compute the determinant of the matrix A via reduction to triangular form. (perform elementary row operations)
Question (7) Consider...
Determine whether the given set S is a subspace of
the vector space V.A. V=C2(ℝ) (twice continuously
differentiable functions), and S is the subset of VV consisting of
those functions satisfying the differential equation
y″=0. B. V=ℙ5, and SS is the subset of ℙ5 consisting of those polynomials satisfying
p(1)>p(0)C. V=ℙ4, and SS is the subset of ℙ4 consisting of all polynomials of the form
p(x)=ax3+bx.D. V=Mn×n(ℝ), and SS is the subset of all
symmetric matrices.E. V=ℝ2, and S consists of...
please can you give the solutions not just anwsers. Thank
you.
1 LetE CR E : x + x2 - X3 = 1, be an affine subspace. Select one or more: 1. The affine subspace ECR is passing through the point (0,3,2) il E = aff((1,0,0), (2,0,1),(1, 1, 1)) l. The affine subspace H CR' perpendicular to E and passing through the point (1,2,3) is given by H -(1,2,3) + lin((3,3, -3)) W. The Image of the affine orthogonal projection...
linear algebra 2 parts mcq
part a
part b
Solve the system 5 = ;3x - ܕܠ ܐ2 + X1 13 = 3xa - ܕ2xn + X -X+ X2 ܂3 1 xto tec b. Xt tec SE N 51 0 d. XS ܢܬ ܝ ܝ SEC e X=S <. [ f. x=s H Let be the set of third degree polynomials H = {ax + ax? + ax | AEC} Is H a subspace of ? Why or why not?...
3. Is each of the following is a subspace of R4? If yes, find a basis A. The set of all (x1, z2, s, z4) that satisfy both 2x1-32 o 51 +22 30 B. The set of all (x1,22, z3, z4) that satisfy both 5x1+22 3 0
3. Is each of the following is a subspace of R4? If yes, find a basis A. The set of all (x1, z2, s, z4) that satisfy both 2x1-32 o 51 +22 30...
(1 point) Determine whether the given set S is a subspace of the vector space V. A. V = R", and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed mxn matrix. B. V is the vector space of all real-valued functions defined on the interval (-oo, oo), and S is the subset of V consisting of those functions satisfying f(0) 0 C. V Mn (R), and S is the...
Find a subset of S which is a basis of the vector space V. (a) V = R3, S = = {(!),()()($).():(})} (b) V = P3(R), S = {1+ 2x, 1 + x + x2, 2+x - x2, 3+2x, * - 2x3}
a. Let W and X both be subspaces of a vector space V. Prove that dim(WnX) > dim(W) + dim(X) - dim(V) b. Define a plane in R" (as a vector space) to be any subspace of dimension 2, and a line to be any subspace of dimension 1. Show that the intersection of any two planes in R' contains a line. c. Must the intersection of two planes in R* contain a line?
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