Chapter 3: 2P (page 88)
As in Problem 1, write out in detail in terms of equations like (2.6) for two equations in four unknowns; for four equations in two unknowns.
The form iswhich can be written as:
The form is
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Write the matrices which produce a rotation about the axis, or that rotation combined with a reflection through the (y,z) plane.
In Problems,use to show that the given functions are linearly independent.
(a) Prove that. Hint: See.
(b) Verify (9.11), that is, show that (9.10) applies to a product of any number of matrices. Hint: Use (9.10)and (9.8).
Use the method of solving simultaneous equations by finding the inverse of the matrix of coefficients, together with the formula for the inverse of a matrix, to obtain Cramer’s rule.
In (9.1) we have defined the adjoint of a matrix as the transpose conjugate. This is the usual definition except in algebra where the adjoint is defined as the transposed matrix of cofactors [see (6.13)]. Show that the two definitions are the same for a unitary matrix with determinant
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