Science:Math Exam Resources/Courses/MATH152/April 2016/Question B 02 (a)

MATH152 April 2016

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Question B 02 (a)
In the system below, $x$, $y$, and $z$ are variables, and $a$ and $b$ are constants. ${\begin{array}{ccccccc}x&+&y&+&z&=&5\\x&~&~&+&z&=&1\\ax&~&~&+&z&=&b\end{array}}$ (a) Write the system as an augmented matrix.

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
An augmented matrix for a system of equations is a matrix in which each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign) and each column represents all the coefficients for a single variable.

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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. Observe that the given linear system is equivalent with ${\begin{array}{ccccccc}1x&+&1y&+&1z&=&5\\1x&+&0y&+&1z&=&1\\ax&+&0y&+&1z&=&b\end{array}}$ Then, by its definition in the Hint, we can easily find the augmented matrix: $\color {blue}\left({\begin{array}{ccc|c}1&1&1&5\\1&0&1&1\\a&0&1&b\end{array}}\right)$.