The calculator will find the null space of the
2x
3 matrix
[66−332306336], with steps shown.
Solution
The reduced row echelon form of the matrix is [1001−21] (for steps, see rref calculator).
To find the null space, solve the matrix equation [1001−21]⎣⎡x1x2x3⎦⎤=[00].
If we take x3=t, then x1=2t, x2=−t.
Thus, x=⎣⎡2t−tt⎦⎤=⎣⎡2−11⎦⎤t.
This is the null space.
The nullity of a matrix is the dimension of the basis for the null space.
Thus, the nullity of the matrix is 1.
Answer
The basis for the null space is ⎩⎨⎧⎣⎡2−11⎦⎤⎭⎬⎫≈⎩⎨⎧⎣⎡1.414213562373095−11⎦⎤⎭⎬⎫.A
The nullity of the matrix is 1A.