LetA basis for the kernel of A is18AFind bases for the kernel and image of A (or, equivalently, for the linear transformation T(x) = Ax).81118A basis for the image of A is-9 963-231.

Given a linear transformation Tx=Ax , where the matrix A=-96-33-21. To Find :Bases of kernel and…

Answered: Let A basis for the kernel of A is A =…

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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Let TR5 R³ be the linear transformation given by X1 x2 T x3 x4 X5 x1 + 2x2 x3 + 2x4x5 2x14x22x3 + 5x4 + x5 2x14x22x3 + 6x5 (a) Find the image of T and a basis for it. (b) Find the kernel of T and a basis for it. (c) Find the rank and nullity of T. Is the dimension of the domain of T equal to the sum of the rank and nullity that you found?
Suppose that {V₁, V2, V3} is a basis of R³. Let T: R³ R be a linear transformation. Show that there are constants a, b, c ER such that: T(xv₁+yv₂ + 2V3) = ax +by+cz
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Each of the following matrices determines a linear map from R into R3: 1 2 0 1 1 0 2 -1) (1) A = 2-1 2-1 (ii) B = 2 3-1 1 1 -3 2 -2 -2 0-5 3 Find a basis and the dimension of the image U and the kernel W of each map.
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A A basis for the image of A is - 1 2 8 3 -2 O 10 3 -2 0 - Find a basis for the image of A (or, equivalently, for the linear transformation T(x) = Ax).
1. Consider a linear transformation R² → R² described by a matrix 11 18 -6 -10| and a non-standard basis B of R²: A = A. Present a vector w 4-3 4-N = 3 in the coordinates of B, that is, find [w]. B. Find a matrix B describing the transformation A relative to the basis B. C. Use this result in order to compute A³ (don't use a calculator!). Reminder: [J-1] [a b] = c d ad - bc d a

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Let A basis for the kernel of A is A = A basis for the image of A is [3 -9 6 3 -2 Find bases for the kernel and image of A (or, equivalently, for the linear transformation T(x) = Ax), 31.