# 2016math1030cw1sol - 2016 MATH1030 Classwork 1 Suggested...

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2016 MATH1030Classwork 1 Suggested Solution1. Solve the following system of linear equations. State your stepsclearly.(a)2x1-x2= 13x1+ 2x2= 12
Substitute it into equation 1:2x1-3 = 1x1= 2
(b)x1-x2-x3= 02x1+ 3x2-3x3= 11-x1+ 3x2+ 6x3=-1
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2. For the following system of linear equationx1+ 2x2+x4= 1x1+ 2x2+x3+x5= 32x1+ 4x2+x3+x4+2x5= 1(a) Write down the coefficient matrix, the constant vector andthe augmented matrix.
(b) Applying row operations on the augmented matrix, findthe solution set.
Solution set :3
-2x2-x4+ 1x2x4+ 5x4-3x2, x4R3. Either do (i) part a, b(easier) or (ii) part c, d, e (harder)Letb1, b2, b3be constants.For the following system of linearequationsx1+ 2x2+x3+x4=b12x1+x2-x3+ 3x4=b24x1-x2-5x3+ 7x4=b3(a) Givenb1= 1, b2= 1, b3= 3. Show the the system of linearequations has no solution.(b) Givenb1= 1, b2= 1, b3= 1, find the solution set of thesystem of linear equations.(c) Applying row operations on the augmented of the systemof linear equation, transform it into the form10***01***0000*,where*represent numbers.(d) Show that the system of linear equations has empty solu-tion set ifb36= 3b2-2b1.(e) Show that the system of linear equations has non-emptysolution set ifb3= 3b2-2b1. Find the solutions.Answer.4
(We will do (c) first). Use augmented matrix: