4. Recall the weird vector space given in Question 1 of Assignment 2: V = R...

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4. Recall the weird vector space given in Question 1 of Assignment 2: V = R² with operations defined by (u₁, U2)+(V1, V2) = (u₁ +v₁+1, 2+2 -1) k(u₁, u₂) = (ku₁+k-1, kuz-k+1) Let u (1,0), = (-1,0). = (a) Show that (u, v) form a basis in V (you must use these weird operations.) (b) Find the coordinate vectors of (2,0) and (0,0) and (-1, 1) relative to this basis (again, you must use these weird operations.) 4. Recall the weird vector space given in Question 1 of Assignment 2: V = R² with operations defined by (u₁, U2)+(V1, V2) = (u₁ +v₁+1, 2+2 -1) k(u₁, u₂) = (ku₁+k-1, kuz-k+1) Let u (1,0), = (-1,0). = (a) Show that (u, v) form a basis in V (you must use these weird operations.) (b) Find the coordinate vectors of (2,0) and (0,0) and (-1, 1) relative to this basis (again, you must use these weird operations.)

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Step No 1 The vector space V R Given operations are U1 U2 V1 V2 u1 v1 1 u2 v2 1 ku1 ... View the full answer