Question

(1) Give three examples of a system of 3 equations with three variables, one with no solutions, one with a unique solutions and one with infinitely many solutions.

Linear Algebra.

Answer 1

40013 1 2 3 14 Example of linear equations with unique Solution Suppose there is an Augmented Matrix with a 3x3 Identity Matrix on the right A=lioli Now performing any number of Elementary now operations on this kind of Matrix gives a system af linear equations with unique solution x=1, y = 2 z=3 one of them for example is T i l the equation system is x + y + z = 6 x+2y +32=14 hus unique solution x+y -2= Example of a system of equations with Infinitely many Solutions 113 114 1 is an augmented Matrix with Last To -1361-8 To oolol row completely zero If we perform any number of elementary row operations on this kind of a Matrix we get Systems with Infinite Solutions z=t, free variable x and y can be expressed in term of t one of the examples is 113-14 x+3y-2=4 14 -1 28 22 -7 ulo 2x - 2y +48=0 has infinite Solutions Example of Systems with no Solutions The Augmented Matrix of the following form Containing Zeroes all to the right and Non zero at the right 113-1141 After any finite row operations gives a System ooolaz) with no Solutions one of the example is (13-1 la 4-1 28 x+3y-2=4 4x - y + 2y = 8 O -13 6 -8 12-7 u 1-3 uz-y +23=8 has no solutions 24-7y +43 = -3