12. (a) Find the solution(s) to the following system of linear equations:-3.r + 2y + 2z= 5,4y + 4z= 3,-x -2x + 4y= -2.(b) Let R be the region in the positive quadrant bounded by the straight lines4.x, and by the hyperbolas xy = 1 and xy = 3.= 2x and(i) Sketch the region R(ii) Define parameters u =in the (u, v)-plane, corresponding to the region R in the (x, y)-plane.y/x and v = xy. Determine and sketch the region S(iii) Hence, using the given change of variables, evaluate the double integralTxYsin)dA.I =x2

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Find the solution(s) to the following system of linear equations: -3r + 2y + 2z = 5, - 3, —х — 4у + 4z = -2. 2х + 4y

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Systems Of Linear Equations

Section1.1: Introduction To Systems Of Linear Equations

Problem 72E: Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by...

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Question

12. (a) Find the solution(s) to the following system of linear equations:
-3.r + 2y + 2z
= 5,
4y + 4z
= 3,
-x -
2x + 4y
= -2.
(b) Let R be the region in the positive quadrant bounded by the straight lines
4.x, and by the hyperbolas xy = 1 and xy = 3.
= 2x and
(i) Sketch the region R
(ii) Define parameters u =
in the (u, v)-plane, corresponding to the region R in the (x, y)-plane.
y/x and v = xy. Determine and sketch the region S
(iii) Hence, using the given change of variables, evaluate the double integral
TxY
sin
)dA.
I =
x2

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