MAT2705-02/06 09F Quiz 4 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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1a) Write down the coefficient matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EiQUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRicvRjVRJ25vcm1hbEYn, the RHS matrix b and the augmented matrix 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 for this linear system of equations.b) By hand reduce this matrix to its ReducedRowEchelonForm in a few easy steps, annotating the operations you apply to each successive matrix in the process, using the notation: 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 .
[You may use technology to check your steps.]
c) Write out the equations that correspond to the reduced matrix. Identify the leading variables ("L") and the free variables ("F") and solve the system according to the accepted procedure. State your solution in the form:
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d) Check by backsubstitution of your solution into the first equation of the original system that it is satisfied.
2. 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 matrix is the reduced matrix for a 3x5 linear system in the variables 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. Identify the leading variables ("L") and the free variables ("F"). Write out the equations that correspond to the reduced matrix and solve the system, stating your solution as above.
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Notice it solved for the second and third variables instead of the first and second according to our row reduction algorithm below.a) The coefficient and RHS matrices, and the augmented matrix are therefore: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b)Now we reduce the augmented matrix and backsubstitute solve the reduced system: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) 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 are leading variables, 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 are free variables:d)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.c) 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 are leading variables, 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 are free variables: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TTdSMApJNlJUQUJMRV9TQVZFLzE1MjE1OTQ0OFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIy0iJCIlIiIjIiIkRiciIiEiIiIhIiJGJ0YqIiIlISIjISIkRi02Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjE1OTU0OFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCIiJSIiKCIiJDYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyNTAxNlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzAiJCImIiIjIiIkRiciIiEiIiIhIiJGJ0YqIiIlISIjISIkRi1GLCIiKEYoNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyNTAxNlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzAiJCImIiIjIiIkRiciIiEiIiIhIiJGJ0YqIiIlISIjISIkRi1GLCIiKEYoNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyNTc2MFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzAiJCImIiIiIiIhRihGKEYnRihGJyEiI0YoISIiRihGKCIiI0YnRig2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyNTkzMlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSwoIiIjIiIiJiUkX3QzRzYjRighIiImRis2I0YpRiksJkYpRilGKkYoRipGLjYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyNTAxNlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzAiJCImIiIjIiIkRiciIiEiIiIhIiJGJ0YqIiIlISIjISIkRi1GLCIiKEYoNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyNjAzMlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzAiJCImIiIiIiIkIiIjIiIhRichIiJGJ0YnIiIlRishIiQhIiNGKSIiKEYoNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyNjMwNFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzAiJCImIiIiIiIhIiIjRihGJyEiIkYnISIjIiIlRipGKEYrRilGJyIiJDYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjI0MzAxMlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzAiJCImIiIiIiIhRihGKEYnISIiRichIiMiIiNGKUYoRihGK0YnRik2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI0MzE2NFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzAiJCImIiIiIiIhRihGKEYnRihGJyEiI0YoISIiRihGKCIiI0YnRig2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjI3NjQ3MlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzMiJCInIiIiIiIhRigiIiNGKEYoRihGJ0YoRighIiJGKEYoRihGJyIiJCIiJSEiJjYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjI3NjY1NlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiYiJiYlInhHNiMiIiImRig2IyIiIyZGKDYjIiIkJkYoNiMiIiUmRig2IyIiJjYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjI3Njg1NlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiYiJiwmIiIkIiIiJiUkX3QwRzYjIiIjISIjRiosJiIiJUYpJkYrNiNGKUYpRjEhIiY2Ig==