Let me R. Discuss the solutions of the following system of equations withrespect to the values of the parameter m.3x + yz = 1x - 2y + 2z = mx + yz = 1-

It is given that, m∈ℝ. We have to discuss the solutions of the following system of equations with…

Answered: Let m E R. Discuss the solutions of the…

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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1. (a) Use definition of linear transformation to determine whether the transformation T:R? → R³ defined as follows is linear. -y T r+ 2y 2.r – 4y (b) Let T : R" → R" be a linear transformation. i. Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify. ii. Does S(0) = 0 mean that S is linear? If not, can you give a counter-example? (c) Consider the following matrix transformation T : R² → R² defined as a b T d i. If T rotates the 2D space 150° counter-clockwise, and then reflects the result across the new r-axis, find a, b, c, d. ii. What if T reflects the 2D space across the r-axis first and then rotates 150° counter-clockwise? Do you expect to get the same a, b, c, d? Why or why not?
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10. Which of the following points are solutions to the system? (0, 4, 3), (3, 6, 10), (3, 3, 1) x + 2y – z = 5 x – 3y + z = -5 -2x + y – z = -4
3. Let c e R be a constant. Consider the following system of linear equations over R: = 0 3x1 + 4t1 + (c— 2)22 + (2с— 3)3 CI2 + 13 (*). CI2 + X3 = 0 (2)( Determine all values of c so that the system (*) has a unique solution. (b)( If c = 1, find the dimension of the solution set of the system (*).
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Let m E R. Discuss the solutions of the following system of equations with respect to the values of the parameter m. 3x + y z = 1 x - 2y + 2z = m x + y 2 = 1 - -