Question

Show that R^-1(a)R(a) = I, where I is the identity matrix and R(a) is the rotation matrix. This equation shows that the inverse coordinate transformation returns you to the original coordinate system.

 

 

Answer 1

MuPAD can be used to solve both symbolic and numeric types of calculations. MuPAD can be run by entering mupadwelcome in the command window.

 

A matrix can be defined using the matrix function.To simplify a given algebraic expression, the simplify function is used.

 

Define the R matrix:

R:=matrix([[cos(a),sin(a)],[-sin(a),cos(a)]])

Calculate the value value of R^-1(a)R(a):

R^-1*R

 

Simplify the result:

simplify(%)

 

The result obtained is:

Define the R matrix:

R:matrix([[cos(a),sin(a)],[-sin(a),cos(a)]])

 

Calculate the value of R^-1(a)R(a):

R^-1*R

 

Simplify the result:

Simply (%)

The matrixis called identity matrix which can be repreented by I.

 

Thus, we can say that R-1(a)*R(a) = 1.

Thus, we can say that R-1(a)*R(a) = 1.