Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Matrix Representation of Linear Transformations
Consider the matrices
\(\rm A=\left(\begin{array}{rrr} 2 & 2 & 1 \\ 0 & 2 & -1 \\ 0 & 0 & 3 \end{array}\right) \),
\(\rm B=\left(\begin{array}{lll} 2 & 1 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{array}\right)\) Then
1
A and B are similar over field of rational number ℚ.
2
A is diagonalizable over field of rational numbers ℚ.
3
B is Jordan form of A.
4
Minimal polynomial and characteristic polynomial of A are same.