MAT2705-04/05 18F Quiz 5 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 EQUAL SIGNS and arrows 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).1. 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
a) Write down the coefficient matrix A, the RHS matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkmbW92ZXJHRiQ2JS1GIzYmLUkjbWlHRiQ2KFEiYkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y5LyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y+RjovJTBmb250X3N0eWxlX25hbWVHUSVUZXh0RicvRj1RJ25vcm1hbEYnLUkjbW9HRiQ2L1EtJlJpZ2h0QXJyb3c7RidGOi8lLHBsYWNlaG9sZGVyR0Y2RkQvJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zmbi9GWUY2LUYxNiNRIUYnRjpGRA== and the augmented matrix C = <A | 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> for this linear system of equations.b) With technology (identify your choice!), reduce this matrix C step by step to its ReducedRowEchelonForm avoiding fractions, recording the intermediate matrices and row operations for each step (as in 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). You may combine the AddRow operations within a single pivot, reporting only the final matrix.
c) Write out the equations that correspond to the reduced matrix. Identify the leading variables (L) and the free variables (F) and solve. State your solution in the scalar form: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjFGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= = ..., LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0ZARj4= = ..., etc , then right in column matrix form and identify the coefficient vectors of your free variable parameters.
d) Enter the augmented matrix into Maple and by right context panel menu, find the reduced matrix and the solution of the system of equations. Write down exactly what Maple gives you for the column matrix solution and compare with your reduced matrix and solution. They should agree. Do they?solution1.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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the variables are:
Free: 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
Leading: 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 the solution 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with the Student LA commands: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Step by step 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uMjIyMjIyMmVtRicvRkVGXm9GKy1GRzYkUSI0RidGL0YrLUZLNiVGTS1GIzYkLUZHNiVGSUZlbkYvRi9GZ25Gam5GKy1GLDYtUSomdW1pbnVzMDtGJ0YvRjJGNUY3RjlGO0Y9Rj9GXW9GX28tRkc2JFEiNkYnRi9GKy1GSzYlRk0tRiM2JC1GRzYlUSIzRidGZW5GL0YvRmduLUYsNi1RKCZtaW51cztGJ0YvRjJGNUY3RjlGO0Y9Rj9GXW9GX28tRks2JS1GTjYmRlBGUS8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RidGVC1GIzYkLUZHNiVGYm9GXXFGL0YvRmduLUYsNi1RIj1GJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjc3Nzc3OGVtRicvRkVGaHFGXHBGLw==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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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making up this problemWorking backwards to produce this original matrix... 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