15.1: Review
- Page ID
- 67819
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Matrix \(A\) is of size (\(m_1 \times n_1\)) and matrix \(B\) is of size (\(m_2 \times n_2\)). What must be true about the dimensions in order to multiply \(A \times B\)?
The following transformation matrix will move points in \(R^n\) dimensional space. What is \(n\)?
\[\begin{split}
\left[
\begin{matrix}
\sin{(\theta)} & -\cos{(\theta)} & 0 & d_x \\
\cos{(\theta)} & \sin{(\theta)} & 0 & d_y \\
0 & 0 & 1 & d_z \\
0 & 0 & 0 & 1
\end{matrix}
\right]
\end{split}\]
The above matrix rotates around which axis?
In the above matrix, how do the scalar values \(d_x\),\(d_y\),\(d_z\) influence the transformation?
Compute \(2u+3v\) for vectors \(u=(1,2,6)\) and \(v=(4,−1,3)\).
What is a homogeneous system of linear equations?