2. Determine which of the following are subspaces of R3: (a) all vectors of the form...
4. Which of the following subsets of Rare subspaces of R? a) vectors of the form (a, b, 1) b) vectors of the form (a, b, a+2b) c) vectors of the form (a, b, c) where a 2b-c=0
Please answer all if possible. Question 15: Do the vectors below form a basis for R3? If so, explain. If not remove as many vectors as you need to form a basis and show that the resulting set of vectors form a basis for R3. C1 = -- () -- () -- () -- (1) Question 16: Carefully consider if equalities below valid for matrices. For each equality state if there is a restriction on dimensions under which they are...
linear algebra 2. Which of the following subsets of Rare actually subspaces? Justify your answer in terms of the definition and properties of subspaces. (a) The vectors [x y z]" with x + 2y -z = 0. (b) The vectors [a b c]" with a + b + c = 3. (c) The vectors [a+2bb-3b]' where a, b are any real numbers, (d) The vectors [pr] where q.r are any real numbers and p20.
3. Use Theorem 4.2.1 to determine which of the following are subspaces of Ps. (a) All polynomials ao + ajx + azx2 + ax for which ao = 0. (b) All polynomials a+ajx+ax + ax for which (c) All polynomials of the form ao +ajx + azx (d) All polynomials of the form ao + ajx, where ao and a do +a+ az + as-0. a2x2asr which ao, a, a2, and as are rational numbers. real numbers . Which of...
3. Which of the following set of vectors in R3 are linearly independent? (a) (6, -11, 2); (-6, 13, -2), (b) (2,6,6); (2,7,6); (2,7,7), (c) (1,-1,3); (-2,0,5); (3,-1, 1); (2,2,3). Explain your answer. Which of these systems forms a basis in R3.
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)...
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.
6. Let W be the set of all vectors of the form W {(a,b,c): a – 2b + 4z = 0} Is W a subspace of the vector space V = R3?
Question 2. 20 marks Determine whether the following sets form subspaces of the standard 2-dimensional Euclidean space (R%. +. :): (a) A = {(11.12)|*1 = -2). (b) B = {(21,12) 2119 = 0). (e) C = {(1, 12) 12 = 2x;}. (d) D = {(2,12) ||*|-|-2), where x. denotes the absolute value of x, for i=1,2. (e) E = {(*1,22) | } = =3)
Determine if the following sets are subspaces. Explain your answer 1. The unit disk in R2, that is the set {(r, y) E R2 r2y s 2. The plane 2 3y 0 in R3 1)