Find all real triangular matrices A such that A^2 = B
2 21
0 25

 > Matrix!! not det, or absolute value.
How do I approach this? I htought about getting rid of the 25 on the bottom right to make it a triangular matrix. Then what?
Find all real triangular matrices A such that A^2 = B
2 21
0 25

 > Matrix!! not det, or absolute value.
How do I approach this? I htought about getting rid of the 25 on the bottom right to make it a triangular matrix. Then what?
Is this B? If A is an upper triangular matrix $\displaystyle \begin{bmatrix}a & b \\ 0 & c\end{bmatrix}$, then [tex]A^2= $\displaystyle a^2 & ab+ bc \\ 0 c^2\end{bmatrix}= \begin{bmatrix}2 & 21 \\ 0 & 25\end{bmatrix}$.
So you need to solve $\displaystyle a^2= 2$, ab+ bc= 21, and $\displaystyle c^2= 25$. It should be easy to solve for a and c and then you have a simple linear equation to solve or b. Nothing could be simpler!

 > Matrix!! not det, or absolute value.
How do I approach this? I htought about getting rid of the 25 on the bottom right to make it a triangular matrix. Then what?[/QUOTE]
Is this B? If A is an upper triangular matrix $\displaystyle \begin{bmatrix}a & b \\ 0 & c\end{bmatrix}$, then $\displaystyle A^2= \begin{bmatrix}a^2 & ab+ bc \\ 0 & c^2\end{bmatrix}= \begin{bmatrix}2 & 21 \\ 0 & 25\end{bmatrix}$.
So you need to solve $\displaystyle a^2= 2$, ab+ bc= 21, and $\displaystyle c^2= 25$. It should be easy to solve for a and c and then you have a simple linear equation to solve or b. Nothing could be simpler!
???? Even with the "25", that is triangular!
 > Matrix!! not det, or absolute value.
How do I approach this? I htought about getting rid of the 25 on the bottom right to make it a triangular matrix. Then what?