# Matrix binomials please help

1. Jun 8, 2010

### flutterfly

Matrix binomials...please help!!!

Find the general statement that express Mn in terms of aX and bY if:
A = aX and B = bY
$$M = \begin{pmatrix} a+b & a-b \\a-b & a+b \end{pmatrix}$$
M = A + B
M2 = A2 + B2
$$X = \begin{pmatrix} 1 & 1 \\1 & 1 \end{pmatrix}$$
$$Y = \begin{pmatrix} 1 & -1 \\-1 & 1 \end{pmatrix}$$

How would i do this question:... is it a matter of LS and RS check?
Test the validity of your general statement by using different values of a, b, and n?

Last edited: Jun 8, 2010
2. Jun 8, 2010

### lanedance

Re: Matrix binomials...please help!!!

i don't understand your question - note the following tex to help write a matrix
$$A = \begin{pmatrix} a & b \\c & d \end{pmatrix}$$

3. Jun 8, 2010

### Dick

Re: Matrix binomials...please help!!!

What are XY and YX? If you expand (A+B)^n what terms can you eliminate? How can you simplify the remaining terms?

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