Let V = P3 = {o + x + ax + a3x | 0, A, A2,...

 

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Let V = P3 = {ão + α₁x + a₂x² + a3x³ | α0, A₁, A2, a3 € R} be a vector space of polynomials of degree 3. a) Extend the linear independent vectors 1 + x², x − x³ to a basis of P3. (12pt.) b) Let W be a supspace of På spanned by w₁ = x + x², w2 = x − x² ve w3 = x + x² + 2x³. Find the coordinate matrix of u = x − x² + x³ with respect to a basis of W. (13pt.) Let V = P3 = {ão + α₁x + a₂x² + a3x³ | α0, A₁, A2, a3 € R} be a vector space of polynomials of degree 3. a) Extend the linear independent vectors 1 + x², x − x³ to a basis of P3. (12pt.) b) Let W be a supspace of På spanned by w₁ = x + x², w2 = x − x² ve w3 = x + x² + 2x³. Find the coordinate matrix of u = x − x² + x³ with respect to a basis of W. (13pt.)

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Salution 9 P3 90 9 x 9x0xiER Now 1x1 xx3 are linearly i... View the full answer