Suppose T: P3-M2,2 is a linear transformation whose action on a basis for P3 is as follows:3]T(-x³-x²-x) =-6 -2-5 5T(−x²-x) =T(ax³ + bx²+cx+d) =-6 -1-5 5T(x³ + x²94641)-[ 4 ] 7(x+1)-[84]==9-6-3+x+1Describe the action of I on a general polynomial, using a, b, c, and d as constants.-[⁰]00

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Answered: Suppose T: P3-M2,2 is a linear…

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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Suppose R is a linear transformation from M₂x3 to R2, and that we know 0 0 4] 80 -13]) = [2] -4 R([1² Answers: a 8 Find constants a and b so that a b and R R([15 [₁ -6-9 -15 -4 0 47 1 8 80 + b 15 0 -6-9 -12] -15 = -7 0 700 4 -10 -7 15 -
f and g are linear transformations which in matrix form are (0 -4) and (3 3) (2 1) (-5 -4) What is the image of the point (-1,1) under the composite transformation g o f?
Diagonalize the following matrix with a similarity transformation: [5 7 -51 0 4 -1 L2 8 -3] A: = Functions of Diagonaligal
Each of J, K, L, M and N is a linear transformation from R2 to R². These functions are given as follows: J(x1, x2) = (3x1 – 5x2, –6x1 + 10x2), K(x1, x2) = (-V3x2, V3x1), L(x1, x2) = (x2, –x1), M(x1, x2) = (3x1+ 5x2, 6x1 – 6x2), N(x1, x2) = (-V5x1, /5x2).
The vertices of a square are H(0, 2), I(2, 0), J(0, –2), and K(-2,0). Which statements are true of the image of HIJK after the given composition of transformations? Select all that apply. Step 1: (x, y) → (-y, x) Step 2: (x, у) — (Зх, Зу) H" (-2,0) HIJKE H'I'J'K' H'TJ'K'~ H"I"J"K" J" (6, 0) Y = xis a line of symmetry for the HIJK and H"I"J"K"
(c) Obtain the 3x3 transformation matrix that first scales a two-dimensional object by a factor of 2 in the x-direction and then reflects the modified object in the y-axis and finally translates the object by 4 in the x-direction and -3 in the y-direction.
17. Find the 4 by 3 matrix A that represents a right shift: (x1,x2, x3) is transformed to (0, x1,x2, x3). Find also the left shift matrix B from R4 back to R³, transforming (x1,x2, x3, x4) to (x2, x3, x4). What are the products AB and BA?
QI) Write down the transformation T (B} 2, 2, (4} 2

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