Tut1-6 question 2018.PDF - EE2007\/IM2007 Tutorial 1 Linear Algebra Systems of Linear Equations Gaussian Elimination Method Exercise 1 Solve the linear

# Tut1-6 question 2018.PDF - EE2007/IM2007 Tutorial 1 Linear...

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EE2007/IM2007 Tutorial 1 Linear Algebra Systems of Linear Equations, Gaussian Elimination Method Exercise 1. Solve the linear system using the Gaussian elimination method. Exercise 2. Give restrictions ona,b,andcsuch that the linear system is consistent,i.e., has solution(s). Exercise 3. Consider the systemx1− x2+ 3x3x4= 1x2x3+ 2x4= 2(a) Described the solution set where the variablesx3andx4are free.(b) Described the solution set where the variablesx2andx4are free.(c) Show that the two solution sets obtained are equivalent[{(32s − t,2 +s −2t, s, t) KVL/Jan18 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 ifk 6= 1 andk 6=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 form2 31a111b051c(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. EE2007/IM2007 Tutorial 2 Linear Algebra RRE, Matrix Algebra, Inverse, Elementary Matrices  • • • 