Page < 2 of 2 ZOOM + 7x²-6√3xy + 13y² - 64 = 0 ii) Identify the conic section by answering the following questions. Conic section: Center: Angle of rotation (CCW): Major axis length: Minor axis length: iii) Sketch the graph of the conic section. 3) a) Find the equation of the least squares regression line for the data points below. (1,1),(2,3), (4,5) b) Graph the points and the line that you found from a) on the same Cartesian coordinate plane. - - = 4) Use the inner product (u, v) = 2µ₁v₁ + u2v2 in R² and the Gram-Schmidt orthonormalization process to transform {(2, −1), (-2,10)} into an orthonormal basis. (HINT: Steps of the Gram-Schmidt orthonormalization process: 1) B = (V2,W1) {V1, V2}; 2) B' = {w₁, W2} where w₁ = V₁ and w₂ = V2 {W1, W1; 3) B" (W1,W1) Wi {u₁, u2} where u₁ = NOTE: Show each step of the Gram-Schmidt ||Will orthonormalization process separately and clearly. Each step will receive a partial credit accordingly.) Page < 1 > of 2 ZOOM + 1) Answer the following questions by circling TRUE or FALSE (No explanation or work required). i) If A = [1 -2 1] 0 1 6, rank(A) = 3. (TRUE FALSE) LO 0 0] ii) If S = {1,x,x², x³} is a basis for P3, dim(P3) = 4 with the standard operations. (TRUE FALSE) iii) Let u = (1,1) and v = (1,-1) be two vectors in R². They are orthogonal according to the following inner product on R²: (u, v) = U₁V₁ + 2U2V2. ( TRUE FALSE) iv) A set S of vectors in an inner product space V is orthogonal when every pair of vectors in S is orthogonal. (TRUE FALSE) v) Dot product of two perpendicular vectors is zero. (TRUE FALSE) vi) Cross product of two perpendicular vectors is zero. (TRUE FALSE) 2) a) i) Determine which function(s) are solutions of the following linear differential equation. - y (4) — 16y= 0 • 3 cos x • 3 cos 2x -2x • e • 3e2x-4 sin 2x ii) Find the Wronskian for the set of functions that you found from i) as the solution of the differential equation above. iii) What does the result that you found from ii) mean? b) Perform a rotation of axes to eliminate the xy-term from the following conic section equation.