New Jersey City University of Mathematics Linear Algebra 8th Homework Instnictor

Question

New Jersey City University of Mathematics Linear Algebra 8th Homework Instnictor: Dev Dee Date 20th April 2017. T pm, in eles Determine whether the set, together with the standard operations, is a vectorspace. If it is not identify at least one of the ten vector space axious that fails. 1) The set of all quadrate functions whoee graphs pass through the origin. The set (z, la) zis a real namber 3) The set of all 2 x 2 uratrioes of the form The art of all 2 x (60 The set of all 4x4 uautrices of form (6) The set of all 3x3 upper triangular matrioes. Cl-1, 11, the set of all continuous functions defined on the interal I-1. 1l. Problem 2i Le V be the set of all positive real minibers. Determine whether V is a wetor

Explanation / Answer

Ans(1):

We know that quadratic function is given by f(x)=ax^2+bx+c. where c is called y-intercept

given that quadratic equations passes through origin means y-intercept is 0 or c=0

Then function passing through origin becomes f(x)= ax^2 + bx

That equation doesn't form vector space because sume of two such quadratic equation may not be quadratic.

for example if f(x)=x^2+4x and g(x)=-x^2 then f(x)+g(x)=4x

which is linear not quadratic

Hence it fails closure property of vector space

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