The Matrix Is the Reduced Echelon Matrix for a System $$\left[ \begin{array} { l l l l | r } 1 & 8 & 0 & 0 & 5 \\0 & 0 & 1 & 0 & - 13 \\0 & 0 & 0 & 1 & 5 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

question 190

Multiple Choice

The matrix is the reduced echelon matrix for a system with variables x 1 , x 2 , x 3 , and x 4 . Find the solution set of the system. $$\left[ \begin{array} { l l l l | r } 1 & 8 & 0 & 0 & 5 \\0 & 0 & 1 & 0 & - 13 \\0 & 0 & 0 & 1 & 5 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

• A) ( k , 5 \(-\) 8 k , \(-\) 13, 5), where k is any real number
• B) (5 \(-\) 8 k , k , \(-\) 13, 5), where k is any real number
• C) (5 + 8 k , k , \(-\) 13, 5), where k is any real number
• D) ( k , \(-\) 5 + 8 k , \(-\) 13, 5), where k is any real number
• E) inconsistent

Recognize and describe the structure of key functional groups, such as carbonyl groups in aldehydes and ketones.

Analyze and provide the structure of simple and complex organic molecules.

Compare and contrast electrophilicity of carbonyl carbons in different environments.

Understand the principles behind various spectroscopic methods (NMR, IR, Mass, UV) for structure determination and characterization of organic compounds.

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