Show that R-1(a)R(a) = I, where I is the identity matrix and R(a) is the rotation matrix.

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.

Solutions

Expert Solution

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.

Junaid answered 1 year ago

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