Tagged: orthonormal vector
Linear Algebra
12/13/2016
by
Yu
· Published 12/13/2016
· Last modified 08/28/2017
Problem 218
For a real number $0\leq \theta \leq \pi$, we define the real $3\times 3$ matrix $A$ by
\[A=\begin{bmatrix}
\cos\theta & -\sin\theta & 0 \\
\sin\theta &\cos\theta &0 \\
0 & 0 & 1
\end{bmatrix}.\]
(a) Find the determinant of the matrix $A$.
(b) Show that $A$ is an orthogonal matrix.
(c) Find the eigenvalues of $A$.
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Linear Algebra
12/09/2016
by
Yu
· Published 12/09/2016
· Last modified 07/31/2017
Problem 214
Find the inverse matrix of the matrix
\[A=\begin{bmatrix}
\frac{2}{7} & \frac{3}{7} & \frac{6}{7} \\[6 pt]
\frac{6}{7} &\frac{2}{7} &-\frac{3}{7} \\[6pt]
-\frac{3}{7} & \frac{6}{7} & -\frac{2}{7}
\end{bmatrix}.\]
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