If a is a square matrix that satisfies the matrix equation a^2-3a+i=0, where i is the identity matrix, find a^{-1}. If A = \bigl(\begin{smallmatrix} 1 & 2\\ 2 & 1 \end{smallmatrix}\bigr) , find a matrix S such that S^{-1}AS is a diagonal matrix (a)...
Eachnurbsobject has atransformmethod that accepts a matrix using gl-matrix style matrices. Seegl-mat2,gl-mat3, andgl-mat4. For example, to apply a transformation in-place to the previous example: varmat3=require('gl-mat3');varm=mat3.identity([]);mat3.translate(m,m,[3,2,0]);mat...
Show that the vectors: a_1 = \begin{pmatrix} 1\ 3\ -2 \end{pmatrix}, a_2 = \begin{pmatrix} 4\ 5\ 3 \end{pmatrix} are linearly independent. For a given set of orthogonal vectors in V, prove the following identity. Determine if the three vectors...