Question

4a + 5b – 6c = 2

Find the value of a for-3a - 2b + 7c = –15.
-a + 4b + 2c = -13
A. -3
B. -2
C. -1
D. -4

Answer 1

9514 1404 393

Answer:

A. -3

Explanation:

The reduced row echelon form* of ...

`\left[\begin{array}c4&5&-6&2\\-3&-2&7&-15\\-1&4&2&-13\end{array}\right]`

is ...

`\left[\begin{array}ccc1&0&0&-3\\0&1&0&-2\\0&0&1&-4\end{array}\right]`

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.

`a=\frac{\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|}=(147)/(-49)=-3`