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# Give a geometric description of the following systems of equations .pdf

25 Mar 2023
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BSC_COMPUTER _SCIENCE_UNIT-5_DISCRETE MATHEMATICS
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### Give a geometric description of the following systems of equations .pdf

1. Give a geometric description of the following systems of equations Solution unique solution or in other words a common point of intersection is possible if and only if determinant of system of equation is non zero. intersection at a common line is possible if any two of the three system of equation are same but it will have infinite solutions. 1. Det (A) = - 5*(-20+9)-5*(5+9)-1*(-3-12)= 55-70+15=0 No solutions. No common points/line 2. Det(A)= - 3*(120-120)+3*(120-120)-12*(30-30) =0 but eqn3 = 1.2*eqn 2 => two of the three equations are same => infinite solutions and common line of intersection 3. Det(A)= 4(-440+37*12) -12(- 160+4*37)+39(-48+44) =16+144-156=4 Have a point in common. and the point of intersection is x= -65/4, y=4, z=1 4. Det(A)=-5(-20+9)-5(5+9)-1(-3-12)= 55-70+15=0 hence, no solution No common points/line
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