Then, my question is just how to fix the inquiry 2? I"m in doubt what also to do. Can someone describe me, what come do?

The vectors that form a basis because that the column an are are certainly in the shaft space. Friend 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.

Hint:

For the shaft space, pick any kind of (nonzero) column.

For the row space, pick any (nonzero) row.

For the null space, an alert that first and 3rd columns of \$A\$ room equal, which method that

\$\$A\beginbmatrix 1 \\ 0 \\ -1 \\ 0\endbmatrix = 0.\$\$

Other 보다 just using formulas, carry out you know the meanings of this words? To obtain a vector in the column space, take any type of one the the columns that the matrix. To acquire a vector in the row room take any one of the rows of the matrix. A vector in the null room is any type of vector, v, such that Av= 0. That"s the only non-trivial component of (2).

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