Please help me find the matrix X. Justify your answer please.

Question

               2 1 0                   1 0 1
Let A = [ 1 0 1 ] and B = [ 2 0 1 ]
                0 3 0                  0 1 1

Find the matrix X such that (2X + A)^-1 = B.

Answer 1

(2x+a) = B-inverse

 

2x = b-inverse - A

 

x = (b-inverse - A)/2

 

 

To find B-inverse do this:

 

 [1 0 1      |    1 0 0

  2 0 1      |    0 1 0

  0 1 1      |    0 0 1 

 

Do Gaussian Elimination on Matrix B so that you get it

to the identity matrix. BUT you MUST do the EXACT SAME

operations on the identity matrix on the right.

 

When Matrix B becomes the indentity matrix on the left

the matrix on the right transforms FROM the identity matrix

into INVERSE.

 

Plug into the formula to find X