Science:Math Exam Resources/Courses/MATH152/April 2011/Question B 06 (a)

MATH152 April 2011

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Question B 06 (a)
Consider the linear systems described below. In cases (a)-(d), write a single, possible reduced row echelon form of the augmented matrix of the system. Two equations in two unknowns with unique solution ${\begin{bmatrix}2\\3\end{bmatrix}}$.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Recall that a unique solution implies there are no free variables; all pivots are 1.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. For a vector x, with components $x_{1}$ and $x_{2}$, the unique solution is ${\begin{aligned}x_{1}&=2,\\x_{2}&=3.\end{aligned}}$ Since there is a unique solution all pivots must be 1. Since we have two equations in two unknowns we have 2 rows and 2 columns. Therefore the augmented matrix would look like $\left[{\begin{array}{cc|c}1&0&2\\0&1&3\end{array}}\right]$

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