Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
This assignment solution was submitted to Amar Sharma for Finite Element Method course at Aligarh Muslim University. It includes: Coordinate, Transformation, Matrix, Augmented, Identity, Row, Operations, Inverse, Simplified
Typology: Exercises
1 / 5
This page cannot be seen from the preview
Don't miss anything!
Q.No.6.9. Consider the coordinate transformation matrix of problem 6.8 and prove that, A-1=At
Solution:
We can form the augmented matrix and solve with identity matrix on the right side. After performing row operations we can make identity matrix on left side the right side matrix will be inverse of matrix. The augmented matrix is given below.
Realizing that,
Hence the augmented matrix will be simplified and is given below,
Dividing 1st^ and 4th^ row by l and 2nd^ and 5th^ row by m,
Adding 1st^ equation to 2nd^ and 4th^ to 3rd^ gives,
Manipulating a little,
Multiplying 2nd^ and 5th^ equation by,
Gives,
But,
Hence,
And,
Thus,
Putting back the values,
Gives,
Hence,
