Matrix

[normabeatty]

I dont know how to start this:

"Given that A = [[3, -2], [-3, 4]] and I = [[1,0], [0,1]], find the values of (lambda) for which A-(lambda)I has no inverse?"


Thanks.

 

[pka]

"Given that A = [[3, -2], [-3, 4]] and I = [[1,0], [0,1]], find the values of (lambda) for which A-(lambda)I has no inverse?"

You want the determinate \(\displaystyle |A-\lambda I|=0\)

Now \(\displaystyle A-\lambda I=\left( {\begin{array}{lr} {3 - \lambda } & { - 2} \\ { - 3} & {4 - \lambda } \\\end{array}} \right)\)

To find the determinate \(\displaystyle \left| {\begin{array}{*{20}c} a & b \\ c & d \\\end{array}} \right| = ad - bc\)