Questions askedCategory: 2568Why is the answer to Section 1.3 #23 a=1?
Alex asked 2 years ago
1 Answers
Yu Staff answered 2 years ago

Let me first say that the solution in the textbook is wrong.

So if you are wondering whether your solution is correct or not, maybe your is correct.

Or do you want to know how to solve the problem?

Alex replied 2 years ago

I would indeed like to know how to solve this problem. I got an answer but I am not sure that it is correct or that I even used the correct method to solve it.

Yu Staff replied 2 years ago

1. Write the augmented matrix and reduce it.
2. If the homogeneous system has a nonzero solution, then it has at least one free variable.
3. The number of free variables is $n-r$, where $n$ is the number of unknowns and $r$ is rank.
4. So, rank must be less than $3$.
5. Find the value of a so that the rank is $2$.