The calculator will find the inverse of the square
2x
2 matrix
[5121], with steps shown.
Related calculators:
Gauss-Jordan Elimination Calculator,
Pseudoinverse Calculator
Solution
To find the inverse matrix, augment it with the identity matrix and perform row operations trying to make the identity matrix to the left. Then to the right will be the inverse matrix.
So, augment the matrix with the identity matrix:
[51211001]
Divide row 1 by 5: R1=5R1.
[1152151001]
Subtract row 1 from row 2: R2=R2−R1.
[10525351−5101]
Multiply row 2 by 35: R2=35R2.
[1052151−31035]
Subtract row 2 multiplied by 52 from row 1: R1=R1−52R2.
[100131−31−3235]
We are done. On the left is the identity matrix. On the right is the inverse matrix.
Answer
The inverse matrix is [31−31−3235]≈[0.333333333333333−0.333333333333333−0.6666666666666671.666666666666667].A