# Math Help - Confused on this Proof! Has Matrix in it??

1. ## Confused on this Proof! Has Matrix in it??

Suppose that

Where a and b are real numbers. Show that

2. Show us what $A^2=?$ and $A^3=?$.

3. Plato, thats the thing, I don't even know where to start? So I wouldn't even be able to tell you A^(2) and A^(3)? Do I solve it like i would solve a matrix by hand?

4. Originally Posted by Grillakis
Plato, thats the thing, I don't even know where to start? So I wouldn't even be able to tell you A^(2) and A^(3)? Do I solve it like i would solve a matrix by hand?
You must be able to mutilpy matrices in order to work these problems.
$
\left( {\begin{array}{*{20}c}
a & 0 \\
0 & b \\

\end{array} } \right) \cdot \left( {\begin{array}{*{20}c}
a & 0 \\
0 & b \\

\end{array} } \right) = \left( {\begin{array}{*{20}c}
{a \cdot a + 0 \cdot 0} & {a \cdot 0 + 0 \cdot b} \\
{0 \cdot a + b \cdot 0} & {0 \cdot 0 + b \cdot b} \\

\end{array} } \right) = \left( {\begin{array}{*{20}c}
{a^2 } & 0 \\
0 & {b^2 } \\

\end{array} } \right)$

5. Originally Posted by Plato
You must be able to mutilpy matrices in order to work these problems.
$
\left( {\begin{array}{*{20}c}
a & 0 \\
0 & b \\

\end{array} } \right) \cdot \left( {\begin{array}{*{20}c}
a & 0 \\
0 & b \\

\end{array} } \right) = \left( {\begin{array}{*{20}c}
{a \cdot a + 0 \cdot 0} & {a \cdot 0 + 0 \cdot b} \\
{0 \cdot a + b \cdot 0} & {0 \cdot 0 + b \cdot b} \\

\end{array} } \right) = \left( {\begin{array}{*{20}c}
{a^2 } & 0 \\
0 & {b^2 } \\

\end{array} } \right)$
Ok I am really confused now. I thought doing this proof we would have to do these steps:
Basis Step:
Inductive Hypothesis:
Inductive step:

Thats what i thought we would have to use for this problem? Thats why I am confused.

6. Yes, one would do this problem using induction. You are correct about that.
However, that is not the point. In order to do this problem you must learn to do matrix multiplication.
Without knowing how to do that, there is no hope of doing this problem.
So you must learn matrix multiplication. (Note we don’t teach here).

7. Originally Posted by Plato
Yes, one would do this problem using induction. You are correct about that.However, that is not the point. In order to do this problem you must learn to do matrix multiplication.
Without knowing how to do that, there is no hope of doing this problem.
So you must learn matrix multiplication. (Note we don’t teach here).
Ok. Let me see if I get you. For this particular problem, is just solving matrices? We are not using any induction process. Thats what you are saying...right?