Question

Determine whether the vector u belongs to the null space of the matrix A.

Answer 1

The vector u belongs in the nullspace of A if it is nonzero and if it gives the zero vector on the right hand side of the equation.

Answer 2

\[u= \left(\begin{matrix}2 \\ 3\\ 1\end{matrix}\right)\], \[A= \left[\begin{matrix}-2 & 3 & -5 \\ -2 & -2 & 10\end{matrix}\right]\]

Yes or No

Answer 3

I have to show all work.

Answer 4

Take the cross product and see if the nonzero vector, u, gives the zero vector as the product. If it does, then you know that u is in the nullspace of A.

Answer 5

Thank you!