By definition, the inverse of a square matrix, if it exists, must cancel the original matrix via multiplication. This means that (A^-1)A=I, where I is the identity matrix. In the given example, multiply both matrices to verify that the result is the identity matrix and you will see that the -1/2 is necessary. You will eventually see that there is a general formula for the inverse of a 2x2 matrix, again, if it exists.
Isn't the matrix multiplied by it's inverse supposed to equal the identity matrix? Yours doesn't do that? Per this link, among others www.mathwords.com/i/inverse_of_a_matrix.htm
thank you do! dpt free 3 markah
Now I love math even more
Thanks A Lot! :)
how to do the negative half power?
hello , why do you multiply the matrix with -(1/2)
By definition, the inverse of a square matrix, if it exists, must cancel the original matrix via multiplication. This means that (A^-1)A=I, where I is the identity matrix. In the given example, multiply both matrices to verify that the result is the identity matrix and you will see that the -1/2 is necessary. You will eventually see that there is a general formula for the inverse of a 2x2 matrix, again, if it exists.
bruh this is so wrong x^-1 is not x*1/2 wth?
Isn't the matrix multiplied by it's inverse supposed to equal the identity matrix? Yours doesn't do that? Per this link, among others www.mathwords.com/i/inverse_of_a_matrix.htm
It does. You may want to double check your multiplication. ;-)
oh for petes sakes this is why I couldn't do well in any math class. You get one calculation wrong, you get the whole thing wrong. :p you were right