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(Solved): Problem 1: We define the determinant of a matrix in general to be det(A)=\sum_(j=1)^n (-1)^(1+j)a_(1 ...
Problem 1: We define the determinant of a matrix in general to be
det(A)=\sum_(j=1)^n (-1)^(1+j)a_(1j)det(A_(1j))Given this information, find the determinant of the following matrices ANALYTICALLY! (Do not use a calculator). (a)
[[1,2],[3,6]](c)
[[a,b],[0,d]](e)
[[1,-1,0],[0,2,1],[-1,-2,1]](b)
[[1,2],[0,6]](d)
[[1,0,0],[2,3,4],[1,-1,2]](f)
[[a,b,c],[0,e,f],[0,0,i]]Problem 2: Are the following matrices invertible? Explain. (a)
[[1,2],[3,6]](c)
[[a,b],[0,d]](e)
[[1,1,2],[1,-2,-1],[1,1,2]](b)
[[1,2],[0,6]](d)
[[a,b],[c,d]](f)
[[a,b,c],[0,e,f],[0,0,i]]