Given the Characteristic Polynomial, Find the Rank of the Matrix
Let $A$ be a square matrix and its characteristic polynomial is given by
Find the rank of $A$.
(The Ohio State University, Linear Algebra Final Exam Problem)
Note that the degree of the characteristic polynomial […]
Maximize the Dimension of the Null Space of $A-aI$
5 & 2 & -1 \\
2 &2 &2 \\
-1 & 2 & 5
Pick your favorite number $a$. Find the dimension of the null space of the matrix $A-aI$, where $I$ is the $3\times 3$ identity matrix.
Your score of this problem is equal to that […]
Orthonormal Basis of Null Space and Row Space
1 & 0 & 1 \\
0 &1 &0
(a) Find an orthonormal basis of the null space of $A$.
(b) Find the rank of $A$.
(c) Find an orthonormal basis of the row space of $A$.
(The Ohio State University, Linear Algebra Exam […]