Mathematics, 16.11.2019 04:31 toxsicity
Aset v is given, together with definitions of addition and scalar multiplication. determine which properties of a vector space are satisfied (select all that apply.) v is the set of polynomials with real coefficients and degree 2 or less. addition is defined by (a_2x^2 + a_1x + a_0) + (b_2x^2 + b_1x + b_0) = (a_0 + b_0)x^2 + (a_1 + b_1)x + (a_2 + b_2) and scalar multiplication by c(a_2x^2 + a_1 + a_0) = ca_0x^2 + ca_1x + ca_2. property 1: if v_1 and v_2 are in v, then so is v_1 + v_2. property 2: if c is a real scalar and v is in v, then so is cv. property 3: there exists a zero vector 0 in v such that 0 + v = v for all v in v. property 4: property 3 holds and for each v in v there exists an additive inverse vector -v in v such that v + (-v) = 0 for all v in v. property 5(a): for all v_1 and v_2 in v, we have v_1 + v_2 = v_2 + v_1. property 5(b): for all v_1, v_2 and v_3 in v, we have (v_1 + v_2) + v_3 = v_1 + (v_2 + v_3). property 5(c): for all v_1 and v_2 in v and real scalars c_1, we have c_1(v_1 + v_2) = c_1v_1 + c_1v_2. property 5(d): for all v_1 in v and real scalars c_1 and c_2, we have (c_1 + c_2)v_1 = c_1v_1 + c_2v_1). property 5(e): for all v_1 in v and real scalars c_1 and c_2, we have (c_1c_2)v_1 = c_1(c_2v_1). property 5(f): for all v_1 in v, we have 1 - v_1 = v1. none of these
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Aset v is given, together with definitions of addition and scalar multiplication. determine which pr...
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