Let å = 2 (first two ID digits),(middle three ID digits), 1 (last two digits)Let u =(first three digits), v =(last four digits)5 7 45 72 16.Let A =(place your whole ID in each row)9.Calculations.1. Construct projzv. Round each component to four decimal places.I2. Let p = 2+ 3x – x³. Determine the coordinate matrix of p relativeto the basis B = {1,1 – x, 1 + x², 1 – x³}.3. Construct the orthogonal complement S for S = span{u, v}.4. Use the Gram-Schmidt Process to construct an orthonormal basisfor the vector space V = span{a, b, c}.%3DRound answers to four decimal places, where necessary.5. Consider the basis B = {(2,-v2). (2, v2)} for R². Define (ỷ, 2) =y1z1 +y2z2.%3Da) Verify that B is an orthonormal basis.b) Calculate [w, for w (20,-6v2).6. 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.7. Define T: R3 → R³ such that T(a) = (1,2,1), T(b) = (0,1,3),T(C) = (1,0, –1).Calculate T(-2,3,-1).8. Define T: R2 → 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 T-1 relative to the basis {(1,1), (1,2)}.

1. We are given two vectors, u→=0215, v→=7491 .We have to find the projection of v→ onto u→, whose…

(first three digits), v = 1 4 (last four digits) 6. Let u = %3D %3D 5 2 15 7 4 9 Let A = (place your whole ID in each row) L2 1 5 7 4 9 Calculations. 1. Construct projav. Round each component to four decimal places. 2. Let p = 2+ 3x – x³. Determine the coordinate matrix of p relative to the basis B = {1,1 – x, 1+ x², 1 – x³}. %3D

(first three digits), v = 1 4 (last four digits) 6. Let u = %3D %3D 5 2 15 7 4 9 Let A = (place your whole ID in each row) L2 1 5 7 4 9 Calculations. 1. Construct projav. Round each component to four decimal places. 2. Let p = 2+ 3x – x³. Determine the coordinate matrix of p relative to the basis B = {1,1 – x, 1+ x², 1 – x³}. %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let å = 2 (first two ID digits),
(middle three ID digits), 1 (last two digits)
Let u =
(first three digits), v =
(last four digits)
5 7 4
5 7
2 1
6.
Let A =
(place your whole ID in each row)
9.
Calculations.
1. Construct projzv. Round each component to four decimal places.
I
2. Let p = 2+ 3x – x³. Determine the coordinate matrix of p relative
to the basis B = {1,1 – x, 1 + x², 1 – x³}.
3. Construct the orthogonal complement S for S = span{u, v}.
4. Use the Gram-Schmidt Process to construct an orthonormal basis
for the vector space V = span{a, b, c}.
%3D
Round answers to four decimal places, where necessary.
5. Consider the basis B = {(2,-v2). (2, v2)} for R². Define (ỷ, 2) =y1z1 +y2z2.
%3D
a) Verify that B is an orthonormal basis.
b) Calculate [w, for w (20,-6v2).
6. 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.
7. Define T: R3 → R³ such that T(a) = (1,2,1), T(b) = (0,1,3),T(C) = (1,0, –1).
Calculate T(-2,3,-1).
8. Define T: R2 → 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 T-1 relative to the basis {(1,1), (1,2)}.

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