The calculator will find the null space of the
2x
3 matrix
[142137], with steps shown.
Solution
The reduced row echelon form of the matrix is [100171175] (for steps, see rref calculator).
To find the null space, solve the matrix equation [100171175]⎣⎡x1x2x3⎦⎤=[00].
If we take x3=t, then x1=−711t, x2=−75t.
Thus, x=⎣⎡−711t−75tt⎦⎤=⎣⎡−711−751⎦⎤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 ⎩⎨⎧⎣⎡−711−751⎦⎤⎭⎬⎫≈⎩⎨⎧⎣⎡−1.571428571428571−0.7142857142857141⎦⎤⎭⎬⎫.A
The nullity of the matrix is 1A.