How do you find the inverse of #[(8,-3),(4,-5)]#?
Append an identity matrix then solve as if Gauss-Jordan to get
Initial Matrix With Identity:
pivot row = n; pivot column = n; pivot entry augmented matrix entry at (n,n)
1. convert pivot n row so pivot entry = 1 2. adjust non-pivot rows so entries in pivot column = 0
Pivot Row 1 reduced by dividing all entries by 8.00 so pivot entry = 1
Non-pivot rows reduced for pivot column by subtracting appropriate multiple of pivot row 1 from each non-pivot row
Pivot Row 2 reduced by dividing all entries by -3.50 so pivot entry = 1
Non-pivot rows reduced for pivot column by subtracting appropriate multiple of pivot row 2 from each non-pivot row
The last two columns are the required identity matrix.
With a bit of effort the decimal fractions can be converted to the fractions shown in the answer above.