Question

帮手解答吧！大学数学题！

Answer 1

(a)

if ad-bc=0, in other terms, the determinant of this matrix M is nonzero,

thus, the inverse of this matrix exists, and the rank of the matrix is 2

we denotes the inverse of M is M'(we get it by gaussian elimination), s.t. M*M'=I(identical matrix)

so, if we use gaussian elimination, we will get the reduced row echelon form as an identical matrix

(b)

the linear system can be rewritten as follows:

by applying gaussian elimination, we will get an reduced row echelon as follows:

it clearly gets only one solution:

[x,y]=[m,n]

Answer 2

线性代数->初等变换