Question

Suppose that the matrix A is an "almost identity". The columns 1, 3, 4,..., n are the vectors e_1, e_2, e_3,...,e_n respectively. But, the second column is some vector

a₁₂

a₂₂

a₃₂

...

a_n2

with a_22 not equal to 0. Find a formula for the matrix A and find a formula for the matrix A^-1

Answer 1

here we have to form matrix A in which the columns 1,3,4,........ are the vectors e₁,e₂,.........e_n

here e₁={1,0,0,.......,0}

e₂={0,1,0,0,........,0} and e_n={0.0.0...............,1}

but the second column is the vector {a₁₂,a₂₂,.........,a_n2} with a₂₂ not equal to zero

then matrix will look like as acc to the statement

A =

where a is not equal to zero

and if we put a₁=a₂=a₃=......=a_n=0 then we get the "almost identity" matrix