Chapter 1, Problem 23SE

A Givens rotation is a linear transformation from ℝⁿ to ℝⁿ used in computer programs to create a zero entry in a vector (usually a column of a matrix). The standard matrix of a Givens rotation in ℝ² has the form $\left[\begin{array}{cc}a& -b\\ b& a\end{array}\right]$, a² + b² = 1 Find a and b such that $\left[\begin{array}{c}4\\ 3\end{array}\right]$ is rotated into $\left[\begin{array}{c}5\\ 0\end{array}\right]$.

A Givens rotation in ℝ²