Science:Math Exam Resources/Courses/MATH152/April 2010/Question B 01 (b)

MATH152 April 2010

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Question B 01 (b)
Three friends, Hartosh, Mark and Keiko decide to paint houses over the summer. Hartosh paints twice as fast as Mark. Hartosh and Keiko paint a home with six rooms in 8 hours. All three together paint a home with 14 rooms in 16 hours. (b) Write the system you found above in augmented matrix form.

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
The augmented matrix is the matrix A with an extra column, how do we get the numbers for that extra column?

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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. From B1(a) we have that ${\begin{aligned}A={\begin{bmatrix}1&-2&0\\8&0&8\\16&16&16\end{bmatrix}}\end{aligned}}$ and ${\begin{aligned}\mathbf {b} ={\begin{bmatrix}0\\6\\14\end{bmatrix}}.\end{aligned}}$ The augmented matrix for $A\mathbf {x} =\mathbf {b}$ is $[A|\mathbf {b} ]$. This says to take the matrix $A$ and add the vector $\mathbf {b}$ as an extra column. Therefore the augmented matrix is ${\begin{aligned}\left[{\begin{array}{ccc|c}1&-2&0&0\\8&0&8&6\\16&16&16&14\end{array}}\right]\end{aligned}}$