ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: #1procrastinator on January 23, 2012, 11:52:39 am

Title: Find all 2x2 matrices such that A^-1 = A
Post by: #1procrastinator on January 23, 2012, 11:52:39 am: Using $a^2+bc = 1$

$ab+bd = 0$

$ac + cd = 0$

$bd + d^2 = 1$

I got the following:

$<br /><br /><br /><br />\begin{bmatrix}<br />1 & 0 \\<br />k &-1<br />\end{bmatrix}<br /><br />\begin{bmatrix}<br />-1 & 0 \\<br />k &1<br />\end{bmatrix}<br /><br />\begin{bmatrix}<br />1 & k \\<br />0 & -1<br />\end{bmatrix}<br /><br />\begin{bmatrix}<br />-1 & k \\<br />0&1<br />\end{bmatrix}<br /><br />\begin{bmatrix}<br />1 & 0 \\<br />0&1<br />\end{bmatrix}<br /><br />\begin{bmatrix}<br />-1 & 0 \\<br />0&-1<br />\end{bmatrix}<br /><br />$

But the answers also have this:

$<br /><br />\begin{bmatrix}<br />a & b \\<br />\frac{1-a^2}b&-a<br />\end{bmatrix}<br />$

If you can write c as (1-a^2)/b, couldn't you do the same with b?

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