Find all matrices A of the form ⎡⎣⎢000x00yz0⎤⎦⎥ such that AB=BA where B is the matrix ⎡⎣⎢400330−263⎤⎦⎥. Express all such matrices in terms of the free variable z. Some of the entries could be of the form az/b for some scalars a, b in ℝ, b ≠ 0.
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Let matrix A be of the form: \[ A = \begin{bmatrix} 0 & 0 & 0 \\ x & 0 & 0 \\ y & z & 0 \end{bmatrix} \] and matrix B be given as: \[ B = \begin{bmatrix} 4 & 0 & 0 \\ 3 & 3 & 0 \\ -2 & 6 & 3 \end{bmatrix} \] Show more…
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