JSFHMAT2705-01/06 07F Quiz 3 Print Name (Last, First) _________________________________|__Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use arrows and equal signs when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC).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
a) Write down the coefficient matrix A, the RHS matrix b and the augmented matrix C = <A | b> for this linear system of equations.b) Without technology, hand reduce this matrix to its ReducedRowEchelonForm by hand in 5 easy steps, annotating the MultiplyRow, AddRow, SwapRow operations you apply to each successive matrix in the process, using your own words or the notation: 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
c) Write out the pair of equations that correspond to the reduced matrix. Identify the leading variables and the free variables and solve for the leading variables, assigning arbitrary parameters to the free variables. State your solution in the form: 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 .
d) Now check that this solution satisfies the original equations by backsubstituting it into them.
e) Finally check your results with technology (G.C. or Tools Menu, Tutors, Linear Algebra, Linear System Solving), and if incorrect, state the correct results for the reduced matrix and the solution of the system and try to find the error in your hand work (don't erase, cross out).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a) First we make up an integer matrix with small entries that will reduce without fractions so this hand reduction is painless: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So we use this one to state the problem.The coefficient and RHS matrices, and the augmented matrix are therefore: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b)Now we step by step reduce the augmented matrix: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) e) 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 are leading variables, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGPg== is a free variable: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d)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JSFH