nullspace of a matrix | Problems in Mathematics

03/07/2018

Determine Bases for Nullspaces $\calN(A)$ and $\calN(A^{T}A)$

Problem 713

Determine bases for $\calN(A)$ and $\calN(A^{T}A)$ when
\[
A=
\begin{bmatrix}
1 & 2 & 1 \\
1 & 1 & 3 \\
0 & 0 & 0
\end{bmatrix}
.
\] Then, determine the ranks and nullities of the matrices $A$ and $A^{\trans}A$.

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Linear Algebra

03/05/2018

In which $\R^k$, are the Nullspace and Range Subspaces?

Problem 712

Let $A$ be an $m \times n$ matrix.
Suppose that the nullspace of $A$ is a plane in $\R^3$ and the range is spanned by a nonzero vector $\mathbf{v}$ in $\R^5$. Determine $m$ and $n$. Also, find the rank and nullity of $A$.

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