Then, my question is how to solve the question 2? I"m in doubt what even to do. Could someone explain me, what to do?
The vectors that form a basis for the column space are certainly in the column space. You can choose one of these.
You are watching: For the matrix a below, find a nonzero vector in nul a and a nonzero vector in col a.
For the column space, pick any (nonzero) column.
For the row space, pick any (nonzero) row.
For the null space, notice that first and third columns of $A$ are equal, which means that
$$Aeginbmatrix 1 \ 0 \ -1 \ 0endbmatrix = 0.$$
Other than just applying formulas, do you understand the meanings of these words? To get a vector in the column space, take any one of the columns of the matrix. To get a vector in the row space take any one of the rows of the matrix. A vector in the null space is any vector, v, such that Av= 0. That"s the only non-trivial part of (2).
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