33. Define T: R³ → R³ byED-Lx -y + 2zT.2x +3y- zx +2y - 2za. Find all vectors in R that are mapped to thezero vector. 7b. Let w =-6Determine whether there isa vector v in R’ such that T (v) = W.%3D

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Answered: 33. Define T: R³ → R³ by y + 2z 2x +3y…

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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2. Consider the vectors (2, 1,0, 0], [3, 1,0, 0], [0, 0,0, 1] in R'. Find a vector v so that v, [2, 1,0, 0], [3, 1,0, 0], [0, 0,0,1] are linearly independent.
Q/Find the real values of a, b, c that make the convolution equal to zero for the vector function F(x, y, z) = (2az + y – 5x)i + (2x – z + 2cy)k + (y + 2bx + 3z)j
Calculate the curl of the vector = (2x + 3y)i + (y+z)j + (xy + 2zx)k
Express the integral f(x, y, z) dV as an iterated integral in six different ways, where E is the solid bounded by the given surfaces. y = x2, z = 0, y + 2z = 4 f(x, y, z) dz dy dx J-2 Jo f(x, y, z) dz dx dy f(x, y, z) dx dz dy f(x, y, z) dx dy dz f(x, y, z) dy dz dx f(x, y, z) dy dx dz 4-2z
Compute the curl of each of the following vectors: V = (yz, xz, xy) F = (x, y, z) = = ( Note: Y 2 (x² + y² +2²)³/²¹ (x² + y² + x2)³/²¹ (x² + y² + x2)³/2 • If the answer is a scalar, you can just type it in the box (using the Calcpad if you like, or using / for fractions, ^ for exponents, etc.) For multiplication, you can either leave a space, or use *. So x*x=xx = x². Note that this is not the same as xx without a space; that will get read as an entirely different variable! • If you need to enter a vector, enter an ordered list of components, so for A you can enter either A = (A₂, Ay, A₂) = {Ax, Ay, Az} . Note that the system isn't great with multiplying through by overall factors, so it's better not to write e.g. • If you need to enter O, enter it in three components, as (0, 0, 0) or {0,0,0}. V x V = ▼ xr= vx= (2A, 2A, 2A₂).

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33. Define T: R³ → R³ by y + 2z 2x +3y - z x +2y - 2z x - y a. Find all vectors in R' that are mapped to the zero vector.