Determine if the vector mapping T(x): R 2X X T ([x]) = x + x...

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Determine if the vector mapping T(x): R² 2X₁ X₁ T ([x²]) = x ₁ + x₂ X1 --x₁ + 3x₁] Is B = {V₁, V₂, V3 } a basis for R³ ? 2 ----6--13 = 8 = 0 → V3 R3 linear? Consider the following set of polynomials in P3: S = {t²+1, ²+2t, 3t² +t-1}. Find a basis for Span{S}) Determine if the vector mapping T(x): R² 2X₁ X₁ T ([x²]) = x ₁ + x₂ X1 --x₁ + 3x₁] Is B = {V₁, V₂, V3 } a basis for R³ ? 2 ----6--13 = 8 = 0 → V3 R3 linear? Consider the following set of polynomials in P3: S = {t²+1, ²+2t, 3t² +t-1}. Find a basis for Span{S})