Show that the following sets under standard operations are n

Show that the following sets under standard operations are not vector fields. (#11-13) the set of all third degree polynomials set of all 2X2 matrices of the form[1 y x z] V = {(x, y): x Greaterthanorequalto 0 y epsilon R} Examine whether W is a subspace of the vector space V {#14 - 19} W is the set of all points on the line x - 2y = 0 V = R^2 W is the set of all points on the line x - 2y = 5 V = R^2

Solution

11 , 12 ,13

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16 and 17

solutions of the equations are real numbers

we know that set of real numbers form a vector space

so , W form a subspace of vector space