Use elimination to find the triangular factors in A LU if U

Use elimination to find the triangular factors in A = LU, if

Under what conditions on the numbers a, b, c, d are the columns linearly independent?

Solution

Solution- the matrix is given by -

A=

R₄->R₄-R₃ THEN matrix will be-

R₃->R₃-R₂

now R₂->R₂-R₁

now applying the same elementary operation step by step on 4x4 unit matrix as applied on matrix A we will get,

hence LU decomposed matrix A is the multiplication of  the upper two matrices

if a=b=c=d then coulumns are linearly independent