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**1. Homework Statement**

**A)**let T_k be all polynomials with degree 3 or under such that k is their coefficients sum.

so we can say that exist at least 2 values of k for them T_k is the sub vector space of P_3(x)?

**B)**this question is about direct sum: Let [tex]V_1,V_2,V_3[/tex] be subvector spaces of V if [tex]V_1 \cap V_2={0}[/tex] and [tex]V_1 \cap V_3={0}[/tex] than [tex]V_1 \cap (V_2+V_3)={0}[/tex]

## Homework Equations

**A)**is this true??? am i right? look under for my answer

## The Attempt at a Solution

**A)**i think this statment is false for example for k=2,4 we have T_k polynomials but T_k is not close under scalar multipication....is this right?

**B)**i infact dont think the statement is true but i couldnt find an exaple to support it