7. For which condition on b = (b₁,b2, b3) do there exist solution(s) for the linear system Ax = b?2 3 14756 80[1(a) A = 23(b) A =1252 2 312, 6. Check whether Az = b is solvable or not i.e., if the vector b =1 0A = 1 45 3 11[2303215? Justify your answer.23 is in the column space of the matrix

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Answered: 7. For which condition on b = (b₁,b2,…

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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If the linear system has infinitely many solutions, then k=? and h= ?
10. - -) Solve the following system of linear equations by using Cramer's rule. x1 + x₂ + 3 x3 = 0 -x1 + 2x2 + 3x3 = 1 x1 + 3x2 + 2x3 = 1
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?
So, we get a system of linear equations: 91m + 21c = 360 21m + 6c = 95 How to get like this?
For which conditions on b = (b₁, b2, b3, b4) do there exist solution(s) for the linear system Ax = b? 2 3 12 12 (a) A = (b) A = 1 6 4 0 [1 10 8 14 16 2 6 14 1 1 1 2 4 4 06 4 60 4 4 1 6 12 12 4 4 1
4. Use Gaussian elimination with backward substitution to solve the following linear system: 2x1 + x2 – x3 = 5, x1 + x2 – 3x3 = -9, -x1 + x2 + 2x3 = 9;
2. a) Given the following system of linear equations: -6+ 10 *+y+=5 2x-y+=9 x-2y+3z =16 Detemine the values of x, y and z using the Cramer's rule.
What answers this question?
1. given that d^2y/dx^2 + 14 dy/dx +50 y=0. y(0) =2 , y'(0) =-17 Find ; 1)The auxiliary eq 2)The general solution of the differential eq 3)The particular solution

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7. For which condition on b = (b₁,b2, b3) do there exist solution(s) for the linear system Ax = b? 1 2 3 1 2 4 7 5 3 6 8 0 (a) A = (b) A = 1 122 1 5 3