- #1
Kate2010
- 146
- 0
Homework Statement
A is an nxn matrix. Suppose A has the form ([tex]^{U}_{W}[/tex][tex]^{V}_{X}[/tex]) in which U, V, W, X are n1xn1, n1x n2, n2xn1 and n2xn2 matrices respectively, such that n1 + n2 = n. If V=0, show that detA = detUdetX
Homework Equations
detA := [tex]\sum[/tex] [tex]_{\rho\in sym(n)}[/tex] sign ([tex]\rho[/tex])[tex]\Pi[/tex] ai i[tex]\rho[/tex]
The Attempt at a Solution
I don't really know how to go about this. If I expand along the 1st row I will get each of the u entries of the first row multiplied by their minor and sign summed together, and the v coefficients will all be zero. I don't know how to write this using the correct notation or where I would go from here.