Checking if a Bilinear Operation is an Inner Product Prove whether or not the following operation defines an inner product in R²: (u, v) = x1 y1 x1Y2 − x2Y1 + 3x2Y2 where u = (x1, x2),v= (31,392)
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- Give example T2 space but not T3 SpaceFind projvu and projuv. Use the Euclidean inner product. u = (-1, 2, 1), v = (1, 2, 1) (a) projvu (b) projuvLet A = {1, 2, 3} and B = {1, 3, 5}. Let A x B denote the Cartesian product of A and B. Indicate if the statement is true or false. (2, 2) = A x B O True (5, 1) A × B O True A x B has six elements B x A = A x B O True O False False False O True O False
- Show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3). ⟨u, v⟩ = u1v1 − 2u2v2 + u3v3The scalar product 0v is 0.I have performed the following polynomial multiplication in matlab on two vectors of polynomial coefficients v1 and v2. What is the degree of the output polynomial? mymult = conv ( v1, v2 )mymult=3 45 -6 -78 -99 65 -54 -12 -10 240 9 10 8 11 7