9514 1404 393
Answer:
A. -3
Step-by-step explanation:
The reduced row echelon form* of ...
[tex]\left[\begin{array}{ccc|c}4&5&-6&2\\-3&-2&7&-15\\-1&4&2&-13\end{array}\right][/tex]
is ...
[tex]\left[\begin{array}{ccc|c}1&0&0&-3\\0&1&0&-2\\0&0&1&-4\end{array}\right][/tex]
which tells you the value of 'a' is -3.
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* Many scientific and/or graphing calculators and web sites can find the reduced row echelon form of a matrix for you. Or, for a single variable (such as 'a'), you can use Cramer's rule. That requires you compute two 3×3 matrix determinants. Again, there are many calculators, apps, and web sites that will make this calculation for you.
[tex]a=\dfrac{\left|\begin{array}{ccc}2&5&-6\\-15&-2&7\\-13&4&2\end{array}\right| }{\left|\begin{array}{ccc}4&5&-6\\-3&-2&7\\-1&4&2\end{array}\right|}=\dfrac{147}{-49}=-3[/tex]
