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Null space of $$$\left[\begin{array}{cc}7 & 24\\0 & 1\end{array}\right]$$$
Your Input
Find the null space of $$$\left[\begin{array}{cc}7 & 24\\0 & 1\end{array}\right]$$$.
Solution
The reduced row echelon form of the matrix is $$$\left[\begin{array}{cc}1 & 0\\0 & 1\end{array}\right]$$$ (for steps, see rref calculator).
To find the null space, solve the matrix equation $$$\left[\begin{array}{cc}1 & 0\\0 & 1\end{array}\right]\left[\begin{array}{c}x_{1}\\x_{2}\end{array}\right] = \left[\begin{array}{c}0\\0\end{array}\right].$$$
Since this system has a unique solution, the null space contains only a zero vector.
The nullity of a matrix is the dimension of the basis for the null space.
Thus, the nullity of the matrix is $$$0$$$.
Answer
The null space is $$$\left[\begin{array}{c}0\\0\end{array}\right]$$$A, it has no basis.
The nullity of the matrix is $$$0$$$A.