MAT280 Fall2020 TakeHome 119 update - WordRiley CyronRCMailingsReviewViewHelpA ShareHomeInsertDesignLayoutReferencesLet å =(first two ID digits), =(middle three ID digits), 2=| 1 (last two digits)Let i =(first three digits), v =(last four digits)1 57 49Let A =(place your whole ID in each row)15 7 4 9 1Calculations.1. Compute (u, 3).Determine ||v||. Write the answer as a simplified square root.3. Calculate the angle between u and v in radians.Round answer to four decimal places.4. Construct projzv. Round each component to four decimal places.5.Let p = 2+3x - x3. Determine the coordinate matrix of p relativeto the basis B = {1,1 – x, 1 + x²,1 – x3}.6. Construct the orthogonal complement S for S = span{u, v}.7. Use the Gram-Schmidt Process to construct an orthonormal basisfor the vector space V = span{d, b, č}.Round answers to four decimal places, where necessary.8. Consider the basis B = {(2, -V2), (2, V2)} for R?. Define (3, z) =y,z1 +y22.%3Da) Verify that B is an orthonormal basis.b) Calculate [w], for w = (20,-6V2).9. Define a linear transformation T: R → R² by T(X) = Ax.Calculate the image of (1, 0, 2, 1, 2, -1, 1, 2).b) Calculate the pre-image of (60, 120).c) Determine a basis of the range of the transformation.d) Determine a basis for the kernel of the transformation.10. Define T: R3 → R such that T (à) = (1,2,1), T(b) = (0,1,3),T(C) = (1,0,–1).Calculate T(-2,3,-1).11. Define T: R? → R² by T(x, y) = (3x – 2y, y – 2x).a) Construct the standard matrix for T.b) Construct the matrix for T relative to the basis {(5,2), (2,1)}.c) Construct the matrix for T1 relative to the basis {(1,1), (1,2)}.in 74

Question

Accepted Answer

The given vectors are:
u→=0215 and v→=7491