I. Consider the set of all 2 × 2 diagonal matrices: D2 under ordinary matrix addition and scalar multiplication. a....
linear algebra 1. Determine whether the given set, along with the specified operations of addition and scalar multiplication, is a vector space (over R). If it is not, list all of the axioms that fail to hold. a The set of all vectors in R2 of the form , with the usual vector addition and scalar multiplication b) R2 with the usual scalar multiplication but addition defined by 31+21 y1 y2 c) The set of all positive real numbers, with...
Math 287, ME/MQ 01 3. Consider the set W of all 2 x 2 matrices of the form with the standard operations of matrix addition and scalar multiplication (a) Show that this set is closed under the operation of addition, (b) Ifu,EW and c is a real munber, show that cu + v) cu + cv. (c) Display the zero vector for W.
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...
i want answers of all Questions Example. As another special case of examples we may regard the set R of all of n umber vector 1.4.6. Example. Yet another al l the vector space M of mx matrices of members of where m - NI. We will use M. horthand for M F ) and M. for M.(R) 1.4.9. Exercise. Let be the total real numbers. Define an operation of addition by y the maximum of u and y for...
I just need an example of a vector space that is closed under scalar multiplication but not under addition. That is all. Thanks for your wisdom.
LO 2a 4) Let V be the set of diagonal 2x2 matrices of the form la ). Determine whether or not this set is a subspace of the set of all real-valued 2x2 matrices, M22, with standard matrix addition and scalar multiplication. Justify your answer.
Let n EN Consider the set of n x n symmetric matrices over R with the usual addition and multiplication by a scalar (1.1) Show that this set with the given operations is a vector subspace of Man (6) (12) What is the dimension of this vector subspace? (1.3) Find a basis for the vector space of 2 x 2 symmetric matrices (6) (16)
2. Consider the following set of complex 2 x 2 matrices where i = -1: H = a + bi -c+dil Ic+dia-bi Put B = {1, i, j, k} where = = {[ctdie met di]|1,3,c,dex} 1-[ ), : = [=]. ; = [i -:], « =(: :] . (a) Show that H is a subspace of the real vector space of 2 x 2 matrices with entries from C, that is, show H is closed under matrix addition and multi-...
(1 point) The trace of a square n x n matrix A = (aii) is the sum ani + 022 + ... + ann of the entries on its main diagonal. Let V be the vector space of all 2 x 2 matrices with real entries. Let H be the set of all 2 x 2 matrices with real entries that have trace 1. Is Ha subspace of the vector space V? 1. Does H contain the zero vector of...
Need to use all axioms to prove this is a vector space. e(a+b)z and scalar multiplication as feax a E R} define addition as ea* + ebx ekax where k e R. Is V a vector space under these definitions? If so, what is the 0 element = eaeba- 8. Let V = k ea of V? e(a+b)z and scalar multiplication as feax a E R} define addition as ea* + ebx ekax where k e R. Is V a...