How does the determinant of this problem expand according to the first line? Detailed steps

Obviously, it is more convenient to expand this question according to the first column, or according to the nth row. It's a bit "unreasonable" for you to ask for the first line.

1) The first line contains two elements: a 1 1= 1, and a 12= 1.

2) Determine the cofactor: M 1 1 is the determinant after removing the elements in the rows and columns of a 1 1.

m 1 1 = | 1 1 0...0|

0 1 1 ...0|

............

0................... 1 (one order lower than the original determinant)

Similarly, M 12=|0 1 0...0|

0 1 1 ...0

................

100 ... 1 (also in the order of n- 1)

3) determine the algebraic cofactor a11= [(-1) (1+1)] * m1= m1/.

a 12=[(- 1)^( 1+2)]*m-2=-m 12

4) According to the determinant expansion theorem, expand the determinant according to the first line.

dn = a 1 1a 1 1+a 12a 12+a 13a 13...+a 1nA 1n

= 1 * m 1 1+ 1 * a 12+0 ...

=M 1 1-M 12

=1:This is the upper triangle -(- 1) (n-2) RN- 1. It takes n-2 exchanges to switch to r 1.

= 1+(- 1)^(n- 1)