Applying a 3x3 matrix to a set of 4 coordinates
Hi, I'm struggling with this question on a practice exam.
I have to apply the product of two 3x3 matrices, to a set of 4 coordinates for a square and explain the transformation. Putting the coordinates into a matrix gives me a 2x4 matrix. From my understanding, a 3x3 matrix cannot be applied to a 2x4 matrix, so I'm stuck on how to proceed.
1 Answer
I am guessing that you are applying a linear transformation to map the 4 corners of a square. The linear transformation is a $3 \times 3$ matrix, say $A$. Coordinates of the square, $P_1, P_2, P_3, P_4$ are points in $\mathbb{R}^3$. In order to find the transformation of the square, you need to find transformation of the corners. Indeed you need to compute
\[PAP_i, i=1,2,3,4\]
which are the transformations of the corners of the square under the map $A$. Note that the above matrix multiplication makes sense, and we are applying a $3 \times 3$ matrix, by a vector in $\mathbb{R}^3$.
Erdos
- 1 Answer
- 386 views
- Pro Bono
Related Questions
- [Linear Algebra] Spectrum
- [ eigenvalues and eigenvectors] Prove that (v1, v2, v3) is a basis of R^3
- Determine values of some constant which equate linear operators whose linear transformation is through a different basis of the same vector space.
- Show that the $5\times 5$ matrix is not invertable
- Linear Algebra Question
- Certain isometry overfinite ring is product of isometries over each local factor
- Find a vector parametric form and symmetric form, find minimal distance betwen L and P, consider vectors v and w.
- Let $H$ be the subset of all 3x3 matrices that satisfy $A^T$ = $-A$. Carefully prove that $H$ is a subspace of $M_{3x3} $ . Then find a basis for $H$.
