u 5 v u 2 u 2 v v u v R set u 2 s 2 t v t the solution set in partb is

U 5 v u 2 u 2 v v u v r set u 2 s 2 t v t the

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KVL/Jan19
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Exercise 4.Determine the values ofksuch that the linear systemkx+y+z=0x+ky+z=0x+y+kz=0has(a) a unique solution(b) a one-parameter family of solutions (i.e., one free variable)(c) a two-parameter family of solutions (i.e., two free variables)[ Unique solution ifk6= 1 andk6=-2;one-parameter family of solutions ifk=-2;two-parameter family of solutions ifk= 1;]Exercise 5.Find the interpolating polynomialp(t) =a0+a1t+a2t2that passes throughthe points (1,12),(2,15),(3,16).[a0= 7, a1= 6, a2=-1 ]Exercise 6.The augmentation matrix of a linear system has the form-231a11-1b05-1c(a) Determine the values ofa,bandcfor which the linear system is consistent.(b) Determine the values ofa,bandcfor which the linear system is inconsistent.(c) When it is consistent, does the linear system have a unique solution or infinitelymany solutions?(d) Give a specific consistent linear system and find one particular solution.
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