Today in Mathland, we learned about how to make inverses of matrices. An in inverse of a matrix or (A^-1) when multiplied to the matrix it is an inverse of or (A) becomes an identity matrix of the same dimensions. They can be multiplied in any order. The steps to do this includes:
1) link the matrix you want to make an inverse of with an identity matrix of the same dimensions
2) use matrix rules to manipulate the matrix so that the left side becomes the identity matrix while the right becomes an inverse matrix.
3) then you can multiply the inverse with its inverse to see if it makes an identity matrix.
If the left side of the bottom row becomes all zeroes, it is a singular matrix with no inverse matrix. Below, i have examples of both normal and matrices with no solution: (the first one is singular and has no solution while the second one is normal and has a solution)
Thanks for examples of both a normal matrix and a singular matrix. These examples helped me with understanding which one is which. It also helped me when to know when to stop for a singular matrix. Thanks for writing down step by step on how to find an inverse. It helped a lot. You explained it very well. Thanks again!
ReplyDeleteI'm glad you explained how to tell when a matrix is singular. I was confused on that and this really helped me a lot. Also your step by step process was very thorough.
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