Use the functionsin Cl-1, 1] to find8/ for the inner productOa 4.8)= 19b.S. g) =g) =180Ob.80c. S.O a. S.8)=QUESTION 17Find the kemel of the linear transformation T: R3 + R, defined by T(x, y, z)= (3x, 0, z)ker(T) = (0, 5,0)}, where s is any real numberb. ker(T) = (r, 0, 0)}, where r is any real number. ker(T) = {(0, 0, 0)}d. ker(7) = {(7, 5, 0)}, where r and s are any real numberse, ker(T) = {(0, s, t)}, where : and t are any real numbersaQUESTION 18Use the standard matrix for the linear transformation T: R² +R° defined by T(x, y)= (4x - 6y, 5x +2y, y) to find the image of the vector V= (2, -2).O a. 7(2, -2) = (-4, 14, 2). 7(2, -2) = (6, -2, 20)TO -=(18 16 2)

The question 16 is not clear. And in question 18 some options are missing.

QUESTION 17 Find the kernel of the linear transformation T: R³ → R³, defined by T(x,y,z)=(3x,0, z) a, ker(7) = ((0, s,0)}, where s is any real number b. ker(7) = ((r, 0, 0)}, where r is any real number c. ker(7) = {(0, 0, 0)} d. ker(7) = {(r, 5, 0)}, where y and : are any real numbers O . ker(T) = {(0, 5, t1)), where : and t are any real numbers QUESTION 18 Use the standard matrix for the linear transformation T: R R³ defined by T(x,y)= (4x – 6y, 5x + 2y, y) to find the image of the vector v= (2, –2). а. Т2, -2) - (-4, 14, 2) ь. Т(2, -2) - (6, -2, 20) TO -=(18 16 2)

QUESTION 17 Find the kernel of the linear transformation T: R³ → R³, defined by T(x,y,z)=(3x,0, z) a, ker(7) = ((0, s,0)}, where s is any real number b. ker(7) = ((r, 0, 0)}, where r is any real number c. ker(7) = {(0, 0, 0)} d. ker(7) = {(r, 5, 0)}, where y and : are any real numbers O . ker(T) = {(0, 5, t1)), where : and t are any real numbers QUESTION 18 Use the standard matrix for the linear transformation T: R R³ defined by T(x,y)= (4x – 6y, 5x + 2y, y) to find the image of the vector v= (2, –2). а. Т2, -2) - (-4, 14, 2) ь. Т(2, -2) - (6, -2, 20) TO -=(18 16 2)

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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