The following three equations define three planes:[br][math] \epsilon_{1}: a_{1} \cdot x + b_{1} \cdot y + c_{1} \cdot z = d_{1} [/math][br][math] \epsilon_{1}: a_{2} \cdot x + b_{2} \cdot y + c_{2} \cdot z = d_{2} [/math][br][math] \epsilon_{1}: a_{3} \cdot x + b_{3} \cdot y + c_{3} \cdot z = d_{3} [/math][br][br][b]Exercise[/b][br]a) Vary the sliders for the coefficient of the equations and watch the consequences.[br]b) Adjust the sliders for the coefficients so that[br][list][*] two planes are parallel, the third plane intersects the other two planes,[br][/*][*] three planes are parallel, but not coincident,[br][/*][*] all three planes form a cluster of planes intersecting in one common line (a sheaf),[/*][*] all three planes form a prism,[/*][*] the three planes intersect in a single point.[/*][/list]c) For each case, write down:[list][*]the equations, [/*][*]the matrix form of the system of equations, determinant, inverse matrix (if it exists)[/*][*]the equations of any lines of intersection[/*][*]any observations you make[br][/*][/list]