Question: Given ( A=left[begin{array}{ccc}1 & 2 & 1 0 & -2 & -1end{array} ight] ) and ( B=left[begin{array}{ccc}1 & 0 & 1 -1 &

Given \$ A=\\left[\\begin{array}{ccc}1 & 2 & 1 \\\\ 0 & -2 & -1\\end{array}\ ight] \$ and \$ B=\\left[\\begin{array}{ccc}1 & 0 & 1 \\\\ -1 & 2 & -5\\end{array}\ ight] \$ (a) (1 mark) Compute \$ A B^{T} \$. Answer: \$ \\left[\\begin{array}{cc}2 & -2 \\\\ -1 & 1\\end{array}\ ight] \$ (b) (3 marks) Find all symmetric matrices \$ X \$, if any, that satisfy \$ A B^{T}(I-X)=0 \$. Answer: \$ X=\\left[\\begin{array}{cc}1+t & t \\\\ t & 1+t\\end{array}\ ight] \$ where \$ t \\in \\mathbb{R} \$

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