Linear Algebra 7e: Counting Solutions of a Linear System

[darrenpeck]

Perfect summary, and before Gaussian Elimination has been demonstrated. Just wonderful! Thank you so much

[sviatoslavlavrinchuk]

Dr. Grinfeld's said: "A unique solution is not possible for systems where there are fewer equation than the number of unknowns".
But what about the case when (for example in R2 for simplicity) the column vector after "=" (b in Ax = b) is colinear with the first column vector, and all other column vectors are colinear with each other but not colinear with the first column vector and b.
For example:
A = [
[1, 3, 6, 9],
[2, 5, 10, 15]
]
b = [2, 4]. Here the only solution to. Ax=b is [2, 0, 0, 0].

[chilly]

It occurred to me that the vectors must be linearly independent by inspection. You have two irrational numbers, root7 and pi - the infinite precision of these numbers surely precludes forming linear combinations of one from the others even with irrational coefficients?

[ahmedhemani]

The instructor says that the space is three dimensional and there are four vectors. To me, it looks like it is a four dimensional space (x, y, z and t) and three vectors.