Homework Answers
Any query then comment below...
Note that any line or plane passing through origin always a subspace...
This means part a) is subspace of R^3 ....
Now
B) ...
Given plane is z= 2..
This plane is not subspace ...because if z1 = 2 and z2 = 2 ..then
az1 + bz2 not equal to 2 for all values of a and b.... So this is not subspace...
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1. Determine whether each of the subsets below are subspaces of R3. (a) The line through...
Determine whether each of the subsets below are subspaces of R3. (a) The line through (2,-5,...
Determine whether each of the subsets below are subspaces of R3. (a) The line through (2,-5, 3) and the origin. (b) The plane parallel to the x, y plane two units above the origin.
Determine whether each of the subsets below are subspaces of R3. (a) The line through (2,-5, 3) and the origin. (b) The plane parallel to the x, y plane two units above the origin.
I. Determine whether each of the subsets below are subspaces of R. (a) The line through...
I. Determine whether each of the subsets below are subspaces of R. (a) The line through (2,-5,3) and the origin. (b) The plane parallel to the z, y plane two units above the origin.
I. Determine whether each of the subsets below are subspaces of R. (a) The line through (2,-5,3) and the origin. (b) The plane parallel to the z, y plane two units above the origin.
I. Determine whether each of the subsets below are subspaces of R. (a) The line through...
I. Determine whether each of the subsets below are subspaces of R. (a) The line through (2,-5,3) and the origin. (b) The plane parallel to the z, y plane two units above the origin.
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace of R3. Justify your answer. (b) For the subsets...
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace of R3. Justify your answer. (b) For the subsets which are subspaces, find a basis and the dimension for each of them
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace...
10. Det ermine whether the following subsets W are subspaces of the given vect or spaces:...
10. Det ermine whether the following subsets W are subspaces of the given vect or spaces: (a) The set of 2 2 matrices given by W. A є M2.2 : A- as a subset of V M2,2 (b) The set of all 3 x 3 upper triangular matrices as a subset of V-M33- (c) The subset of vect ors in R3 of the for (2+x3, r2, r3). (d) The subset of vect ors in R2 of the form (ri,0) (e)...
Name: Math 23 6. (14 points) Determine whether the following subsets are subspaces of the given...
Name: Math 23 6. (14 points) Determine whether the following subsets are subspaces of the given veeto r space. Either prove that the set is a subspace or prove that it is not (a) The subset T C Ps of polynomials of degree less than or equal to 3 that are of the form p(x)-1+iz+o2+caz3, where c,02, c3 are scalars in R. (b) The set s-a a,bERM22, that is, the subset of all 2 x 2 matrices A where a11-a22...
QUESTION 2. (a) Decide whether each of the following subsets of R’ is a subspace. Either...
QUESTION 2. (a) Decide whether each of the following subsets of R’ is a subspace. Either provide a proof showing the set is a subspace of R3, or provide a counterexample showing it is not a subspace: [9 marks] (i) S= {(x, y, z) ER3 : 4.0 + 9y + 8z = 0} (ii) S = {(x, y, z) E R3 : xy = 0} (b) Determine for which values of b ER, the set S = {(x, y, z)...
21. Show that if l is any line through the origin in R3 and x is...
21. Show that if l is any line through the origin in R3 and x is any vector with its initial point at the origin, then the reflection of x through the line & (acting as a mirror) is equal to 2(proj,x) - x, where r is any nonzero vector parallel to the line (see Figure 1.21). Reflection of x FIGURE 1.21
1. For each of the following statements, declare whether the statement is true or false, (a)...
1. For each of the following statements, declare whether the statement is true or false, (a) A system of four linear equations in three unknowns cannot have a solution. (b) 3.x + 3y - 2z = 0 is the equation of a plane through the origin in R', with normal vector (3,3. -2) (c) It is possible to determine if two lines in R3 intersect by solving an appropriate system of linear equations. (a) Find the parametric equation of the...
Show that each of the following subsets are not subspaces by finding a counterexample. (a) The...
Show that each of the following subsets are not subspaces by finding a counterexample. (a) The set of polynomials of degree exactly 2, as a subset of P. (b) The set of polynomials p(q) in P, such that p(1) = 1, as a subset of P. (c) The set of sequences with non-negative terms, as a subset of S.
Determine whether each of the subsets below are subspaces of R3. (a) The line through (2,-5, 3) and the origin. (b) The plane parallel to the x, y plane two units above the origin.
Determine whether each of the subsets below are subspaces of R3. (a) The line through (2,-5, 3) and the origin. (b) The plane parallel to the x, y plane two units above the origin.
I. Determine whether each of the subsets below are subspaces of R. (a) The line through (2,-5,3) and the origin. (b) The plane parallel to the z, y plane two units above the origin.
I. Determine whether each of the subsets below are subspaces of R. (a) The line through (2,-5,3) and the origin. (b) The plane parallel to the z, y plane two units above the origin.
I. Determine whether each of the subsets below are subspaces of R. (a) The line through (2,-5,3) and the origin. (b) The plane parallel to the z, y plane two units above the origin.
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace of R3. Justify your answer. (b) For the subsets which are subspaces, find a basis and the dimension for each of them
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace...
10. Det ermine whether the following subsets W are subspaces of the given vect or spaces: (a) The set of 2 2 matrices given by W. A є M2.2 : A- as a subset of V M2,2 (b) The set of all 3 x 3 upper triangular matrices as a subset of V-M33- (c) The subset of vect ors in R3 of the for (2+x3, r2, r3). (d) The subset of vect ors in R2 of the form (ri,0) (e)...
Name: Math 23 6. (14 points) Determine whether the following subsets are subspaces of the given veeto r space. Either prove that the set is a subspace or prove that it is not (a) The subset T C Ps of polynomials of degree less than or equal to 3 that are of the form p(x)-1+iz+o2+caz3, where c,02, c3 are scalars in R. (b) The set s-a a,bERM22, that is, the subset of all 2 x 2 matrices A where a11-a22...
QUESTION 2. (a) Decide whether each of the following subsets of R’ is a subspace. Either provide a proof showing the set is a subspace of R3, or provide a counterexample showing it is not a subspace: [9 marks] (i) S= {(x, y, z) ER3 : 4.0 + 9y + 8z = 0} (ii) S = {(x, y, z) E R3 : xy = 0} (b) Determine for which values of b ER, the set S = {(x, y, z)...
21. Show that if l is any line through the origin in R3 and x is any vector with its initial point at the origin, then the reflection of x through the line & (acting as a mirror) is equal to 2(proj,x) - x, where r is any nonzero vector parallel to the line (see Figure 1.21). Reflection of x FIGURE 1.21
1. For each of the following statements, declare whether the statement is true or false, (a) A system of four linear equations in three unknowns cannot have a solution. (b) 3.x + 3y - 2z = 0 is the equation of a plane through the origin in R', with normal vector (3,3. -2) (c) It is possible to determine if two lines in R3 intersect by solving an appropriate system of linear equations. (a) Find the parametric equation of the...
Show that each of the following subsets are not subspaces by finding a counterexample. (a) The set of polynomials of degree exactly 2, as a subset of P. (b) The set of polynomials p(q) in P, such that p(1) = 1, as a subset of P. (c) The set of sequences with non-negative terms, as a subset of S.
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