Find General Statement of Matrix Binomials & Test Validity with LS/RS Check

[flutterfly]

Matrix binomials...please help!

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

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?

 

[lanedance]

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

 

[Dick]

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