Finding the inverse of matrices larger than 2x2

[dwn]

Is there a way without using the algorithm to find A^-1 of a square matrix greater than 2x2?

The question we are given in the books is:

[-25 -9 -27]
[536 185 537]
[154 52 143]

We are asked to find A^-1 of the second and third column without computing the first column.

(Sorry about the format...I couldn't figure out how to use the brackets on this one.)

Thanks.

 

[Bipolarity]

A brute force way to do it would be to assume the inverse has 9 variables as its entries and solve the linear system AA^{-1} = I You will get a 3by3 matrix equation which gives you 9 (hopefully independent) equations which you can solve using a 9 by 10 augmented matrix. The solutions will be the entries of the inverse matrix.

BiP

 

[dwn]

We just started the course 2 weeks ago and I'm trying to organize all the theorems we've learned thus far. But it looks like we've only learned to use the algorithm for A^-1 -- reducing the matrix [A I] for matrices larger than 2x2.

I arrived at the answer by [A I₃]

[-25 -9 -27 1 0 0]
[546 185 537 0 1 0]
[154 52 143 0 0 1]

and removing the first column of the identity matrix since they only asked for the second and third column.

Do you have any advice on learning and memorizing all the theorems in LA? I mean is that the best method to grasp LA?

Thanks!